Problem

At serve, a tennis player aims to hit the ball horizontally. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is "launched" from a height of 2.50 m? Where will the ball land if it just clears the net (and will it be "good" in the sense that it lands within 7.0 m of the net)? How long will it be in the air? See Fig. 3-54.

Problem 64GP

Step-by-step solution

Step 1 of 5</p>

As the ball will follow the parabolic path, we need to use the equation of kinematics to determine the magnitude of velocity and time.

Step 2 of 5</p>

Considering the origin to be located on the ground directly underneath the ball and the upward direction to be the positive y direction.

The required equation to determine the value of speed is,

Here h is the height from which the ball is launched, is the height of the net, t is the time, g is the acceleration due to gravity, and , is the initial velocity along the vertical direction.

The value of time is defined as the ratio of distance and velocity.

where v is the minimum speed.

Step 3 of 5</p>

Substituting 0 for , for the equation and solve for

Substituting 9.8 m/s2 for g, 2.5 m for h, 0.9 m for , 15 m for s, we get

Therefore, the minimum speed with which the ball must be served to just clear the net is .