Physiscs problem, Please help!?

Question

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 15.0 m/s at an angle of 50.0° 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.) http://edugen.wiley.com/edugen/courses/crs1507/art/qb/qu/c03/ch03p_40.gif

Answer 1

1.Compute vertical (Vv) and horizontal (Vh) components ball’s velocity
Vv=V sin(50)
Vh=V cos(50

2. Compute the time it takes to reach the max height of the trajectory

t1=Vv/g where g=9.81 m/s^2
We know that H= .5gt1^2 (max height)
t2= sqrt(2(H-2.1)/g)
t2= sqrt(2(.5 g t1^2 -2.1)/g)
t2=sqrt( [Vsin(50)/g]^2 – 4.2/g)


3. t(total) - total time the ball would have to travel to reach the 2.1m (return point)

t(total)=t1+t2

Now computing the speed of the player

4. V=S/tp
S=S1+S3 – 10m
S1=Vht1=V cos(50) t1
S2=Vht2 = V cos(50) t2
And
tp=t(total)-.3 sec

Just do the math

Answer 2

∫ Σ xk *dx; I hope it helps, be happy!