Tennis Projectile Motion Question

[Emethyst]

Homework Statement

A tennis ball is served horizontally at a height of 2.4m, 12m from a net that is 0.9m high. a) If it is to clear the net by at least 0.2m, what is its minimum initial velocity? b) If it clears the net by 0.2m, where will it land? Neglect air resistance for both parts.

Homework Equations

Kinematic equations, d=vt

The Attempt at a Solution

I solved this question, but I'm not sure if I went about doing it right, especially for part b). For a) I set the initial vertical velocity to zero, found time using the equation d=v₀t + (1/2)at², and then used this value of time in the equation d=vt to find the initial (horizontal) velocity, which I calculated to be 23.3m/s. For part b) I essentially did the same as a), making the initial vertical velocity zero, calculating the time, and then plugging it into d=vt with the horizontal velocity from part a) to solve for the distance from the net. I wondering for part b) if this would be correct, for I think that the ball would have some form of initial vertical velocity because of gravity, yet my answer of 11.0m seems to make sense in the context of tennis. If anyone can show me which way would the correct method here it would be greatly appreciated, thanks in advance.

 

[rl.bhat]

In the second part they have asked the horizontal distance between the serving point to the landing point. So find the time taken by the to fall through 2.4 m. use this time to find the distance.

 

[tomcue]

I would first confirm the assumptions made in this problem. Neglecting air resistance means that we are assuming the ball is not affected by the air's resistance as it travels through the air. This is a reasonable assumption for a tennis ball, since it is relatively small and light compared to other objects (such as a baseball or golf ball) that would experience significant air resistance.

Next, I would check the equations used to solve the problem. The kinematic equations are applicable for motion with constant acceleration. In this problem, the ball is only experiencing the constant acceleration of gravity in the vertical direction, but its horizontal velocity remains constant. Therefore, we should only use the kinematic equations for the vertical motion in part a) and use the equation d=vt for the horizontal motion.

For part b), we can use the same approach. The initial vertical velocity will not be zero, but we can still use the kinematic equation d=vt for the horizontal motion. The distance from the net can be calculated by adding the displacement in the horizontal direction (12m) to the horizontal distance traveled by the ball in the time it takes to reach the net (which can be found using the vertical motion equation).

Overall, your approach seems to be correct, but it would be helpful to clarify the assumptions and equations used in your solution.