Question

A ball is hit with a bat, causing it to travel straight upward. It takes 3.20 s for the ball to reach its maximum height after being hit. Treat upward as the positive direction.(a)What is the ball's initial velocity (in m/s), just after it is hit? m/s upward(b)What height (in m) does it reach above the level where it was hit? m

Answer 1

(a) 31.36 m/s upward

(b) 50.18 m

Explanation:

(a)

We can calculate the value of the final velocity by means of the acceleration equation, just like this:

`a=(v_f-v_i)/(t)`

At the maximum height, the velocity is 0. Therefore:

`\begin{gathered} a=(-v_i)/(t) \\ v_i=-a\cdot t,a=g=9.8m/s^2 \\ \text{ Replacing} \\ v_i=-(-9.8)\cdot(3.2) \\ v_i=31.36\text{ m/s} \end{gathered}`

(b)

The height can be calculated using the following formula:

`\begin{gathered} d=v_i\cdot t+(1)/(2)a\cdot t^2 \\ \text{ Replacing:} \\ d=31.36\cdot3.2+(1)/(2)(-9.8)(3.2)^2 \\ d=100.36-50.18 \\ d=50.18\text{ m} \end{gathered}`