Question

A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.20 s for the ball to reach its maximum height.(a) Find the ball's initial velocity. ______m/s upward(b) Find the height it reaches. _______m

Answer 1

(a) 31.36 m/s

(b) 50.2 m

Explanation:

Given:

Time (t) = 3.2 s

At the maximum height, the velocity is 0

Final velocity (v) = 0 m/s

(a)

We can calculate the initial velocity as follows:

`\begin{gathered} a=(v-u)/(t) \\ \\ \text{ we replacing} \\ \\ -9.8=(0-u)/(3.2) \\ \\ u=9.8\cdot3.2 \\ \\ u=31.36\text{ m/s} \end{gathered}`

(b)

Now the distance is determined with the following formula:

`\begin{gathered} d=ut+(1)/(2)at^2 \\ \\ \text{ We replacing:} \\ \\ d=(31.36)(3.2)+(1)/(2)(-9.8)(3.2^2) \\ \\ d=100.352-50.176 \\ \\ d=50.176\approx50.2\text{ m} \end{gathered}`