Maximum height of a ball thrown straight up calculator. Both its velocity and its acceleration point downward.
Maximum height of a ball thrown straight up calculator. (b) Calculate the velocity of the ball when it hits the ground. 45. A ball is thrown into the air at an angle of 60 above the horizontal with an initial velocity of 40 m/s from a 50m high building. The maximum height of the object in projectile motion depends on the initial velocity, the launch angle and the acceleration due to gravity. Projectile motion involves objects that are dropped, thrown straight up, or thrown straight down. 1 second and observe when the height is no longer a positive number v/32 seconds. When the ball is thrown upwards, it initially gains height, reaches a maximum point, and then falls back down. In our case, it's 7 m/s. This force does some amount of work on the ball. Jul 26, 2024 · To find the maximum height of a ball thrown up, follow these steps: Write down the initial velocity of the ball, v₀. Use the kinematic equation for vertical motion without acceleration to find the time it takes for the ball to reach its maximum height. Feb. Jul 31, 2024 · It was not an easy endeavor because such a leap required him to go up in a special balloon and wear a custom-designed spacesuit that protected him from sudden shifts in temperature (after all, he was jumping from the edge of space). Which of the following statements about the direction of the velocity and acceleration of the ball as it is going up is Question: Estimate the maximum height in feet that you can throw a baseball straight up. How much additional time will pass before the ball passes the tree branch on the way back down? Nov 8, 2020 · To find the highest point where the object is thrown, we need to look for the vertex of the quadratic function, h(t) = -16t 2 + 64t + 60, where t = time (in seconds) and h = height (in feet). 6 H = (15) 2 ⇒ H = (15) 2 19. A ball is thrown vertically upwards. 3. From the displacement equation we can Transcribed Image Text: A ball is thrown straight up into the air. Output: The Calculator calculates: Projectile Equations used in the Calculator and Solver. (a) Calculate the time it takes the tennis ball to reach the spectator. The height of the ball in the photograph is given as \(\text{1,5}\) \(\text{m}\) above the initial point. 5at^2}{t} \] where A ball is thrown straight up with a speed of 30 m/s, and air resistance is negligible. 5 m/s), and \(a\) is the acceleration due to gravity (-9. A ball is thrown straight up with an initial speed of 5. 071 kg is thrown straight up with an initial speed v 0 = 11 m/s. 8 m/s/s), and s is the distance covered. Problem: A tennis ball of mass m = 0. (b) Find the time it reaches the maximum height. Hint: Calculate the height after every 0. Where . Our projectile motion calculator is a tool that helps you analyze parabolic projectile motion. 36 - Estimate the maximum height in feet that you can throw a baseball straight up. A ball is thrown straight up from the ground. 8 m/s². The projectile will decelerate on its way to maximum height, come to a complete stop at maximum height, then starts its free fall descent towards the ground. Take the ground to be y0 = 0. There are 2 steps to solve this one. 5m We can use here the general relationship from kinematics: color(red)(v_f^2=v_i^2+2a(y_f-y_i)) where: v_i is the initial velocity=15m/s; v_f is the final felocity which is zero in our case; a is the acceleraton of gravity g=-9. So, the ball gets the maximum height 2 seconds after is is thrown straight up. 4 days ago · The calculator will then process these inputs, giving you the maximum height your projectile will attain under ideal conditions. 2 s? A tennis player wins a match at Arthur Ashe stadium and hits a ball into the stands at 30 m/s and at an angle 45° above the horizontal (Figure \(\PageIndex{4}\)). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). h(x) is the height of a ball thrown upward at 6. 0 m/s. It goes to a height of 20 m and then returns to the ground. Question: A ball is thrown straight up from the ground. Find the momentum of the ball (a) at its maximum height. 29 (a) We analyze two-dimensional projectile motion by breaking it into two independent one-dimensional motions along the vertical and horizontal axes. 00, (c) 1. ) How long does it take the ball to reach the maximum height? (b. To solve this particular case of projectile motion, all you need to enter are the initial velocity, angle, and height. Both its velocity and its acceleration point downward. Note that because up is positive, the initial velocity is positive, as is the maximum height, but the acceleration due to gravity is negative. Replace both in the following formula: h_max = h₀ +(v₀)²/ 2g where g is the acceleration due to gravity, g ~ 9. t = -b/2a. A ball is thrown horizontally from the top of a 60. The parameters involved in projectile motion include duration, maximum height, distance, initial velocity, and angle. A person standing on the edge of a high cliff throws a rock straight up with an initial velocity of 13. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Type in the initial height from which the motion starts. m. (b) How long would it take to reach the ground if it is thrown straight down with the same speed? Sep 22, 2019 · If you throw a ball upward, what happens to it? Unless you can throw the ball at 11. b)The maximum height the ball reached from the base of the building Oct 29, 2024 · Let's assume we want to calculate the time of flight and distance traveled by a ball ⚽ thrown from the Eiffel tower with a horizontal speed only, e. 25 seconds to reach a height of 36. Use the formula for the axis of symmetry to find the x-coordinate of the vertex. The maximum height is reached when \(\mathrm{v_y=0}\). Study with Quizlet and memorize flashcards containing terms like A ball is thrown straight up, reaches a maximum height, then falls to its initial height. 00 m. Calculate the maximum height of the ball, the ball Calculate the time and height at which two bodies, thrown vertically upward one after the other with the same speed, will collide. The act of throwing a ball upward can be studied in two stages. Question: The height of a ball thrown straight up into the air can be modeled by h(t)=−16t2+28t+3. Question: A ball thrown vertically upward reaches a maximum height of 30 meters above the surface of Earth. 50, and (d) 2. What is the difference in height after the ball has been in flight for 1 second and when the ball reaches its maximum height, where t is the for the fall to reach the maximum height and v/g? A ball is thrown straight up from ground level. Set the equation equal Apr 16, 2016 · I found 11. g. (b) How long a time would it take to reach the ground if it is thrown straight down with the same speed? Jan 3, 2008 · A 0. Write a function that determines the maximum height of the ball. Using this we can rearrange the velocity equation to find the time it will take for the object to reach maximum height \[\mathrm{t_h=\dfrac{u⋅\sin θ}{g}}\] where \(\mathrm{t_h}\) stands for the time it takes to reach maximum height. This video uses the vertex point of a parabola to find the maximum height of ball th Let's break it down using the context of the exercise where a ball is thrown straight up and takes 2. a) How long does it take the ball to reach the maximum height? b) What is the maximum height reached by the ball? (a) At what speed does the ball hit the ground? (b) For how long does the ball remain in the air? (c)What maximum height is attained by the ball? 3. 8 × H ⇒ 19. 6 m/s initial vertical component of velocity will reach a maximum height A ball thrown up vertically returns to the thrower after 6 seconds. b) You are asked how long (time) it takes the ball to reach the ground (position), so you want to use equation 1. The Vertical Collision Kinematics Calculator is designed to solve a specific problem related to the collision of two bodies. Write down the initial height, h₀. ) Calculate the maximum height reached by the ball. At this maximum height, the ball’s vertical velocity is zero, but gravity is still acting on it with a constant force of 9. (b) The horizontal motion is simple, because a x = 0 a x = 0 and v x v x is thus constant. Throughout its motion, the ball's velocity is zero. 5 where h(t) is the height of the ball in feet t seconds after it is thrown. For example, if the velocity of the rock is calculated at a height of 8. Projectile vertical motion: formula for maximum time. 3 m. (a) Find the maximum Learn how to calculate the height of a projectile given the time in this Khan Academy physics tutorial. 2 s? The height function here is quadratic, \[h(x) = -16x^2 + 80x\], representing a parabola. To calculate the maximum height, substitute t= 2 seconds into the given formula H(t) = -16*2^2 + 64*2 + 80 = 144 feet. 48 m Hence, the Nov 27, 2016 · A ball is thrown upward from roof of 32 foot building with velocity of $112$ ft/sec. The maximum height formula of an object undergoing projectile motion is: H max = (U 2 Sin 2 θ) / 2g. Let the gravitational potential energy be zero at the initial height of the tennis ball. The question relates position and velocity, so you want to use equation 3. , A dropped ball, starting from rest, accelerates downward. θ = Angle of projection. Questions-Part (a) What is the maximum height, h in meters, the ball reaches? 9: You throw a ball straight up with an initial velocity of 15. 2 s 4. Question: 2. The maximum height reached is h = 5m. ) Determine the time at which the ball pass a point 25. g = Gravitational acceleration = constant = 9. (a) How long is the ball in the air? What is its speed after 4. Use the vertical motion model, h = -16t2 + vt + s where v is the initial velocity in feet/second and s is the height in feet, to calculate the maximum height of the ball. Note also that the maximum height depends only on the vertical component of the initial velocity, so that any projectile with a 67. Select all the answers that describe its motion. Use the slider to change the x-value. (a. Strategy. The height after $t$ seconds is: $s(t)=32+112t-16t^2$. ) What is the maximum height reached by the ball? (c. Use the quadratic function h(t)=−16t^2+109t to find how long it will take for the ball to reach its maximum height, and then find the maximum height. ) cannonball will come back down and land with a speed of 860 m/s, which means that a) everyone ought to stand back, and (b) if the shot was truly vertical, the returning cannonball might smash your cannon. 00 s. Example Enter the initial velocity of the ball: 34 The maximum 7: (a) Calculate the height of a cliff if it takes 2. Which of the following is true about the direction of the ball's velocity and acceleration betweeB and C? V=0 a=0 Sep 26, 2022 · You throw a ball straight up into the air at 18 m/s from a height of 32 m above the ground. Round your answers to the nearest tenth Study with Quizlet and memorize flashcards containing terms like For objects in free fall, select all the answers that are correct. 5\), height is 100 feet. (numerical value and unit) b. Find step-by-step Physics solutions and your answer to the following textbook question: A $0. 10-\mathrm{kg}$ ball is thrown straight up into the air with an initial speed of $15 \mathrm{~m} / \mathrm{s}$. Hint: calculate the height after every 0. Taking acceleration due to gravity g to be 10 m/ s 2. The program should request as input the initial height,h feet, and the initial velocity, v feet per second. , 7 m/s. Which of the following statements about the direction of the velocity and acceleration of the ball as it is going down is correct? ( ) Both its velocity and its acceleration point upward. Therefore, at maximum altitude the velocity of the ball must be zero. Jan 1, 2018 · The formula h(t)=-16t+48t+160 represents the height of a ball, T seconds after it is launched. The height of the ball after t secondsis h + vt - 16t^2 feet. Fill in the blank, read surrounding text. How to Derive the Formula for Maximum Height Apr 7, 2017 · A ball is thrown vertically upwards with a velocity of 49m/s calculate the maximum height and time taken to reach maximum height. io Oct 3, 2024 · The maximum height \(H\) of a projectile can be calculated using the formula: \[ H = \frac{v_0^2 \sin^2(\theta)}{2g} \] where: \(v_0\) is the initial velocity in meters per second (m/s), \(\theta\) is the angle of launch in degrees, \(g\) is the acceleration due to gravity, approximately \(9. 1. Jul 28, 2022 · Angle of launch: If we know the initial velocity and one of its components, we can also calculate the angle of launch: α = arccos(V 0x /V 0) = arcsin(V 0y /V 0); Maximum height: At this point, the projectile stops moving up and starts falling, so its vertical velocity component changes from positive to negative; therefore, V y =0. Homework Equations p=mv The Attempt at a Solution okay so i was trying to figure out the height and then cut it halfway. Sep 9, 2022 · Graph the motion of an object which is thrown upward, then use the kinematic equations to find the maximum height the ball reaches as well as the total time Question: Calculate the maximum height that a ball thrown straight up will reach if it is thrown with a velocity of 25 m/s Formula Substitution Answer with Units Show transcribed image text Here’s the best way to solve it. 5 m T = U/g = 49/9. Jan 28, 2024 · Since the ball is at a height of 10 m at two times during its trajectory—once on the way up and once on the way down—we take the longer solution for the time it takes the ball to reach the spectator: \(t = 3. (a) For this height, how long after the ball leaves your hand does it return to your hand? (b) Estimate the distance in feet that the ball moves while you are throwing it, that is, the distance from where the ball is when you start your throw until it The program should perform the following two calculations: a) Determine the maximum height of the ball. 5m A ball is thrown into the air with an initial speed v. 14 kg ball of dough is thrown straight up into the air with an initial velocity of 24 m/s. 5 m. a. Find the initial and final velocity of the ball and also find the time. Its position at 7 instants of time is shown in the figure; the maximum height is reached at position 4. 7 m/s), a is the acceleration due to gravity (-9. (a) Calculate the time the ball takes to hit the ground. c) Calculate the time it takes the ball to hit the ground from its initial position. So we get: 0^2=15^2-2*9. With this time of flight calculator, you can easily calculate the time the projectile remains in the air. how long does it take to return to its starting point, assuming negligible air resistance? calculate the maximum height reached. Write a program to provide information on the height of a ballthrown straight up into the air. (a) Calculate the displacement and velocity at times of (a) 0. 24, 2022 04:19 a. 2. 81 m/s^2\), \(H\) is the maximum height in meters (m). 0 m/s from a third-floor window located 15. Note: The ball will reach its maximum height after v/32 seconds. 06s (b. How Projectile Motion Calculator Works? Input: Firstly, choose an option from the drop-down list, which you need to calculate the projectile motion with that particular parameter. Sep 12, 2023 · (a) It takes the ball 3 seconds to reach the maximum height. Write the number of the formula from the formula sheet you used Write your answer as three parts number unit formula The initial velocity of the ball, u = 15 m/s Acceleration = -g Final velocity, v = 0 m/s Let the maximum height attained by the ball before it begins to fall back = H Using the third equation of motion, v 2 = u 2-2 g H ⇒ 0 = (15) 2-2 × 9. (a) Calculate the height of a cliff if it takes 2. Final Words: Having said all this, the Maximum Height of a Projectile Calculator is a convenient resource for students, professionals, and enthusiasts needing quick, reliable height predictions in projectile motion See full list on calculators. 21 m/s . A ball is thrown vertically upward with a velocity of 20 m/s. 8m/s^2 (downward); y_f is the height reached from the ground where y_i=0. Now, substitute the values according to the selected option. m = 0. 0 m/s at height 1. Gravity is responsible for pulling the ball back down to Earth after it pauses. So Maximum Height Formula is: \(Maximum \; height = \frac {(initial \; velocity)^2 (Sine \; of \; launch\; angle)^2}{2 \times 7. (a) How long does it take the ball to reach the maximum height? (b) What is the maximum height reached by the ball? (c) What is its speed after 4. 0 m above ground. Mar 11, 2015 · Inao Shyamananda. 6 = 11. a) How long does it take the ball to reach the maximum height? b) What is the maximum height reached by the ball? c) What is its speed after 4. Multiple select question. 4 ft/s from a height of 10 feet. Plug in for t and find h. 2 km/s, it will reach some maximum height then start falling. h = -16(6. What is the maximum height the ball reached and also when does the ball return to the ground? a ball is thrown straight up with a speed of 10. 00 s, and 3. The instantaneous speed of any projectile at its maximum height is zero. b) Calculate the amount of time it takes for the ball to reach its maximum height from its initial position. A ball is thrown straight up with a speed of 30 m/s, and air resistance is negligible. , Object A is thrown straight up with an initial velocity of 10 m/s and object B is thrown straight down with an initial velocity 1. Change the units if needed. A ball is thrown straight up with a speed of 30 m/s. Mar 26, 2016 · Whoa! The ball will go up 38 kilometers, or nearly 24 miles. a) Calculate the initial velocity of the ball. Stage 1: When you throw a ball up you apply a force to the ball in the upward direction as long as it is in contact with your hand. 00 s after it is thrown, neglecting the effects of air resistance. Ignore air resistance. Which of the following statements about the direction of velocity and acceleration of the ball as it is going up is correct? a. In your case, a= -16, b= 64, so the function gets the maximum at t = = 2. A ball is thrown straight up, reaches a maximum height, then falls to its initial height. 8 m/s^2, negative because it's acting against the direction of the throw). Not bad for a birthday present. 8 ms-2 or 10 ms-2. The rock misses the edge of the cliff as it falls back to earth. A ball is thrown straight up into the air with a speed of 30. 6)=11. 8 meters. Its unit of measurement is “meters”. To find the initial speed, we need to reorganize the kinematic equation for vertical motion: \[ u = \frac{H - 0. Find step-by-step Physics solutions and the answer to the textbook question You throw a ball straight up into the air at $18 \mathrm{~m} / \mathrm{s}$ from a height of $32 \mathrm{~m}$ above the ground. The vector initial velocity has two components: V 0x and V 0y given by: V 0x = V 0 cos(θ) V 0y = V 0 sin(θ) The vector acceleration A has two components A x and A y given by: (acceleration along the y axis only) A x = 0 and A y = - g = - 9. 500, (b) 1. Maximum Height. As can be seen, the maximum height depends on the initial velocity given to the projectile. b. Now the last question: when the ball hits the ground. Jul 21, 2015 · Vertically, the motion of the projectile is affected by gravity. Question 9 A ball is thrown straight up from point A, reaches a maximum height at point B, and then falls back to point C as Illustrated by the picture below. ( ) Both its velocity and its acceleration point downward. 79\; s \ldotp\) The time for projectile motion is determined completely by the vertical motion. May 29, 2023 · You throw a ball into the air from a height of 5 feet with an initial vertical velocity of 32 feet per second. Dec 3, 2022 · The symbol for maximum height is H max. Plug in 2 for t to find the object's height after being thrown. The higher this velocity, the more height the object will reach. (a) How long does it take the ball to reach the maximum height? Blank 1. Click on the "Calculate" button to determine the projectile. Figure 5. A ball is thrown straight up with a speed of 36m/s. A tennis player wins a match at Arthur Ashe stadium and hits a ball into the stands at 30 m/s and at an angle 45 ° 45 ° above the horizontal (Figure 4. 8 m/s 2 At time t, the velocity has two components given by V x = V 0 cos(θ) and V y = V 0 sin(θ Free Online Projectile Motion Calculator - calculate projectile motion step by step Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Use the kinematic equations to graph the motion of a ball in freefall as well as calculate the maximum height and time in the air when the ball is thrown str In this case, you want to find the starting velocity that gives a maximum height of 3. The equation is: \(v = u + at\), where \(v\) is the final velocity (0 m/s at the highest point), \(u\) is the initial velocity (22. Its velocity points upward and its acceleration points Oct 26, 2011 · Youtube videos by Julie Harland are organized at http://YourMathGal. A ball is thrown straight up with a speed of 30 m/s, and air resistance is negligible. Maximum height is the position at which y-velocity is zero. ) Calculate the time required for the ball to rise to its maximum height. 8 = 5 sec. ) Ater 0. 0 N Question: 1. ) What is its speed after 4. com. Study with Quizlet and memorize flashcards containing terms like Free Fall: When a ball is thrown straight up with no air resistance, the acceleration at its highest point, Free Fall: A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Read on to learn more about the time of flight equations, or simply play with the calculator instead! May 26, 2023 · How do you find the maximum height of a ball thrown straight up? Use the vertical motion model, h = -16t2 + vt + s where v is the initial velocity in feet/second and s is the height in feet, to calculate the maximum height of the ball. 8 N. . 9 s, it passes a height of 121. Jul 28, 2022 · Use this maximum height calculator to find the highest vertical position of an object in projectile motion, using velocity and angle of launch. 0 m from the base of the building. 14). Randomized Variables. 50 above the ground. Which of the following is the correct statement? A. t = -64/2(-16) = -64/(-32) = 2 seconds. 0 m above the point of contact Jul 22, 2024 · How do you calculate how high a ball will go when thrown up? You throw a ball into the air from a height of 5 feet with an initial vertical velocity of 32 feet per second. Factors that influenc the height of these objects include the height from which the objects are dropped or thrown, whether upward/downward velocity is involved, and of course, the pull of gravity downward on the object. After a time of 4. A function named getInput should be used to obtain the values of h and v, and that function should call a function named calculateheight to calculate the height of the ball. b) Determine approximately when the ball will hit the ground. 25) = 625 ft. (a) What is the height of the ball after 0. Draw a sketch. The maximum height reached is h=5 m. 6 = 225 19. Calculate the maximum height reached by the ball. 10 m above the starting point (using the method from Example) when the initial velocity is 13. Question: 3. 25) 2 + 200(6. 2 s? The ball is thrown straight up and will reach a maximum height, at which point its velocity will be zero, before beginning to fall downwards. Theoretically, that 10kg (about 22 lb. The maximum time is the time it takes for the projectile to reach its maximum height. At its maximum height, the speed of the ball is: Answer: 0 m/s. 7 m/s and no air resistance, use the equation v^2 - u^2 = 2as, where v is the final velocity (0 m/s), u is the initial velocity (9. (a) For this height, how long after the ball leaves your hand does it return to your hand? (b) Estimate the distance in feet that the ball moves while you are throwing it, that is, the distance from where the ball is when you start your throw until Maximum height? A parabola reaches its maximum value at its vertex, or turning point. A ball thrown straight up with an initial velocity of 15. 0-m building and lands 100. Enter the velocity. This means that at maximum height, the vertical component of the initial speed will be zero. C. - **Initial Height:** At \(x = 0\), height is 0 feet. 00 m/s. 2 s? llmis 10) A foul ball is hit straight up into the air with a speed of 30. Calculate the time it takes the ball to reach its maximum height, ignoring air resistance. 9m (c. Note: the ball will reach its maximum height after t Determine approximately when the ball will hit the ground. Transcribed Image Text: A foul ball is hit straight up into the air with a speed of 30. calculate the maximum height of the ball Submitted by Daniel G. The fall itself took 15 minutes, and the maximum speed exceeded 800 miles per hour – far over the sound barrier! A person standing on the edge of a high cliff throws a rock straight up with an initial velocity of 13. 5 seconds the ball is at a height of (b) When will the The value seems reasonable enough. 8)=122. 5 second? (Include units in your answers. The maximum height reached is 625 feet. The Eiffel tower is 324 meters (1,063 ft) tall, but the Dec 2, 2019 · A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. B. ANSWER FORMAT: <magnitude> space <unit> EXAMPLE: 10. (b) What is the maximum height reached by the ball? Blank 2. (b) Determine the height of the ball at 0. It can find the time of flight, but also the components of velocity, the range of the projectile, and the maximum height of flight. 0 m/s straight up, a result of \(±3. 8*(y_f-0) and: y_f=(225)/(19. 48 m ⇒ H = 11. - **Maximum Height:** From our earlier calculation, at \(x = 2. Dec 15, 2010 · In summary, to find the maximum height of a ball thrown straight up in the air with a speed of 9. It reaches its highest point and then falls back. Hint: what is supposed to be the velocity when the ball reaches Free Fall: A ball is thrown straight up with a speed of 30 m / s 30~\text{m}/\text{s} 30 m / s, and air resistance is negligible. Find (i) velocity (ii) Maximum height it reaches (iii) Position after 4 seconds Get the answer to this question and access a vast question bank that is tailored for students. A ball is thrown straight up. At the highest point in its motion, the ball's acceleration is zero. 01 second and determine when the height is no longer a positive number. On its way down, the ball is caught by a spectator 10 m above the point where the ball was hit. So how fast is the ball going at the point where it starts falling again? The answer to this question is the key to solving the question. This calculator allows you to determine the unknown parameters of projectile motion using known values. Hit the ground? The ground will be a height of 0. 35 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8. (b) How long would it take to reach the ground if it is thrown straight down with the same speed? The Formula for Maximum Height. calculate the maximum height and time taken to reach maximum height. Find the momentum of the ball of dough halfway to its maximum height on the way up. s. c. 2~\text{s} 4. a) Find the time to reach the top of its path. 00 s, 2. 20 m/s\) is obtained. 071 kg v 0 = 11 m/s. (a) To find the time it takes for the ball to reach the maximum height, we can use the fact that at the maximum height, the velocity of the ball will be zero. H = U 2 /(2g) = (49 2)/(2 x 9. This work done is manifest as the sum of kinetic energy and potential energy of the When we throw a ball upward, gravity acts against the motion, slowing the ball down until it reaches its maximum height. U = Initial velocity. The ball is at rest at its maximum height ( v = 0). H max = Maximum height. Calculate the position and velocity of the rock 1. Oct 29, 2024 · How do I calculate the maximum height of a projectile with θ = 40° and v₀=5 m/s? To calculate it: Start from the equation for the vertical motion of the projectile: y = vᵧ × t - g × t² / 2 , where vᵧ is the initial vertical speed equal to vᵧ = v₀ × sin(θ) = 5 × sin(40°) = 3. It passes a tree branch on the way up at a height of 7. 7: (a) Calculate the height of a cliff if it takes 2. Problem 6: An airplane takes off and flies upward at an angle of 23° with a constant speed of 256 m/s. While the plane is flying upward, a piece of the engine falls off when the plane reaches a height of 880 m. More information. (b) The maximum height reached by the ball is 45 meters.