Chapter 9.2, Problem 35PPE

Solution

(a)

To calculate: The time required by the ball to reach the highest point in its path.

The required value of $a$ is $a\ge 0$ .

Given Information:

The given functions is $h=-4.9t^2+3.8t+0.5$ .

Maximum height is 0.5 m.

Calculation:

Consider the given functions $h=-4.9t^2+3.8t+0.5$ .

Substitute $h=0.5\text{m}$ .

  $\begin{array}{c}0.5=-4.9t^2+3.8t+0.5\\ -4.9t^2+3.8t=0\\ 4.9t^2-3.8t=0\\ t\approx 0.78\end{array}$

Hence, the required time is $t=0.78\text{s}$ .

(b)

To check whether it is possible to find the amount of time that the ball is in air before it hits the court.

It is not possible to find the amount of time that the ball is in air before it hits the court.

Given Information:

The given functions is $h=-4.9t^2+3.8t+0.5$ .

Calculation:

Consider the given function $h=-4.9t^2+3.8t+0.5$ .

But here the distance of the tennis player and the court is not given.

Hence, it is not possible to find the amount of time that the ball is in air before it hits the court.