Question

A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 130 feet per second. After how many seconds does the ball attain its maximum height?

Answer 1

We use the equation of motion,

$v=u+at$.

Here, v is final velocity, u is initial velocity and a = - g (acceleration due to gravity) because ball thrown vertically into air.

At maximum height, the final velocity becomes zero, i.e v = 0.

Thus equation becomes,

 $0=u-gt\\\\t=\frac{u}{g}$.

Given, $u=130\ ft/s$ and we take  $g=9.8\ m/s^2=9.8\times3.2 \frac{ft}{s^2} =32.14\ ft/s^2$.

Substituting these values in above equation, we get

$t=\frac{130\ ft/s}{32.14\ ft/s^2} =4.05\ s$.

Thus, to reach the maximum height the time taken by the ball is 4.05 s.