The lob in tennis is an effective tactic when your opponent is near the net. It

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 lob the ball with an initial speed of 16.5 m/s, at an angle of 53.0

Explanation / Answer

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.

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