Kinematics in 2d and projectile velocity

[Mshah]

Homework Statement

The lob in tennis is an effective tactic when your opponent is near the net. It consists of lofting the ball over his head, forcing him to move quickly away from the net (see the drawing). Suppose that you loft the ball with an initial speed of v = 18.5 m/s, at an angle of = 47.0° above the horizontal. At this instant your opponent is 10.0 m away from the ball. He begins moving away from you 0.30 s later, hoping to reach the ball and hit it back at the moment that it is 2.10 m above its launch point. With what minimum average speed must he move? (Ignore the fact that he can stretch, so that his racket can reach the ball before he does.)

Homework Equations

Kinematics equations.

The Attempt at a Solution

So far, I've gotten the x and y V components and plugged them into this: y=VyT - 1/2 g T ^2 , where Y is the displacement, to find time.

Vy=V sin 47
Vx=V cos 47
2.1=VyT-(1/2)(-9.8)T^2

 

[G01]

Ok you have this started correctly. Now think about the following.

What is the equation of motion for the opponent in the x direction?
(Think of him as moving at a constant speed, this will essentially be his average speed.)

What is the Equation of motion for the ball in the x direction?

Once you have these, you should be able to use both of the equations to solve for the opponents speed.

 

[m2003]

T=0.481 s

I'm not sure what to do next.

Next, you can use the fact that the opponent starts moving away from you 0.30 s later to find the x position of the ball at that time. This can be done using the equation x = VxT, where x is the displacement in the x direction and T is the time. Once you have the x position of the ball, you can use the Pythagorean theorem to find the distance between the opponent and the ball at that time. This distance can then be used to find the minimum average speed that the opponent must move in order to reach the ball at the desired height of 2.10 m. This can be done using the equation v = d/t, where v is the average speed, d is the distance, and t is the time.