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=(u)/(g)`.

Given,
`u=130\ ft/s` and we take
`g=9.8\ m/s^2=9.8*3.2 (ft)/(s^2) =32.14\ ft/s^2`.

Substituting these values in above equation, we get

`t=(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.