A baseball is hit with a bat and, as a result, its direction is completely reversed and its speed is doubled. If the actual contact with the bat lasts 0.31 s , what is the ratio of the acceleration...

A baseball is hit with a bat and, as a result, its direction is completely reversed and its speed is doubled. If the actual contact with the bat lasts 0.31 s , what is the ratio of the acceleration to the original velocity??

Please show step by step.

Asked on by Kelsia2

2 Answers | Add Yours

llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

Before the impact, let the velocity of the baseball was `v` m/s.

After being hit by the bat its velocity is `-2v`

So, change in velocity, `Deltav=v-(-2v)=3v`

 Acceleration is defined as the rate of change in velocity, i.e. actual change in velocity divided by the time taken to change it. Time taken to change velocity is the time of actual contact of the bat and ball, i.e. 0.31 s.

`a=(Deltav)/(Deltat)`

`=(3v)/0.37`
Therefore, `a/v=3/0.31=9.7 s^-1`

So, the ratio of acceleration of the baseball to its original velocity is 9.7.

tutorbest's profile pic

tutorbest | (Level 1) eNoter

Posted on

Let the initial velocity be x m/s

Then the final velocity, v = - 2u m/s
(the minus sign indicates that the direction was reversed and doubled)

Acceleration = (v - u) / t = - 3u / t

Original velocity / Acceleration = - t / 3 = - 0.31 / 3

We’ve answered 318,928 questions. We can answer yours, too.

Ask a question