Question

1. a person throws a tennis ball straight up into the air, releasing it a short height above the ground and catching it at that same height 3.6 seconds later. if air resistance is negligible, determine the maximum height reached by the tennis ball.

Explanation:

Step1: Find the time to reach maximum height

Since the motion is symmetric (up - down), the time to reach the maximum height \(t\) is half of the total time of flight.
The total time of flight \(T = 3.6\ s\). So, \(t=\frac{T}{2}=\frac{3.6}{2}=1.8\ s\)

Step2: Use the kinematic equation \(v = v_0−gt\) to find the initial velocity

At the maximum - height, the final velocity \(v = 0\). Using the kinematic equation \(v = v_0−gt\) (where \(g = 9.8\ m/s^{2}\)), we can solve for the initial velocity \(v_0\).
\(0=v_0 - 9.8\times1.8\), so \(v_0=9.8\times1.8 = 17.64\ m/s\)

Step3: Use the kinematic equation \(v^{2}-v_0^{2}=- 2gh\) to find the maximum height \(h\)

We know \(v = 0\), \(v_0 = 17.64\ m/s\) and \(g = 9.8\ m/s^{2}\). From \(v^{2}-v_0^{2}=-2gh\), we can solve for \(h\).
\(h=\frac{v_0^{2}}{2g}\)
Substitute \(v_0 = 17.64\ m/s\) and \(g = 9.8\ m/s^{2}\) into the formula:
\(h=\frac{(17.64)^{2}}{2\times9.8}=\frac{311.1696}{19.6}=15.876\ m\)

Answer:

The maximum height reached by the tennis ball is \(15.9\ m\)