Tennis Physics problem?

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 v = 18.5 m/s, at an angle of = 46.0° 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.)

Here is a picture.

http://www.webassign.net/CJ/p3-40alt.gif

I'm just really lost, can someone guide me? I'm not looking to get the answer spoon fed to me.

Answer 1

The ball will follow the equations
vx(t)=cos(46)*18.5
x(t)=vx(t)*t
and
vy(t)=sin(46)*18.5-g*t
y(t)=sin(46)*18.5*t-.5*g*t^2

The opponent follows the equations of
x(t)=10+Vx*(t-.3) for t>=.3
where Vx is his average speed to the ball

First, find t when y(t) = 2.1 m.
There will be two roots to the quadratic, the first when the ball passes above 2.1 m and the second when it returns on the other side of the net

2.1=sin(46)*18.5-.5*g*t^2
using g=9.81
t=2.545 seconds

the ball will have traveled the following distance
x(2.545)=cos(46)*18.5*2.545
x=32.7 meters

That means that
32.7=10+Vx(2.545-.3)
Vx=10.1 m/s

Of course, it also means the ball was behind the baseline since the standard tennis court is 11.885 m from net to baseline.

http://www.play-rite.co.uk/downloads/pdf/dimensions/Dimensions_TennisCourt.pdf


j

Answer 2

tennis physics problem

Answer 3

draw a horizontal line 7 long (to the net). Draw the 4.9 angled line. you should be able to get the heigth and subtract it from the net - but start it at 2 high.