Question

What is the speed of a 0.148 kg baseball if its kinetic energy is 107 J ? Answer in units of m/s.

Answer 1

`v ~~38.03` m/s

Explanation:

Given: `KE = 107` J; `m = 0.148` kg

Formula for kinetic energy:`" "KE = 1/2 mv^2`

The units of kinetic energy is Joules:

`1 J = 1 N*m = 1 kg*m/s^2 * m = 1 (kg*m^2)/s^2`

Substitute the knowns into the `KE` equation:

`107 (kg*m^2)/s^2 = 1/2 (0.148 kg) v^2`

Multiply both sides by `2`:

`2/1 *107 (kg*m^2)/s^2 = 2/1 *1/2 (0.148 kg) v^2`

`214 (kg*m^2)/s^2 = (0.148 kg) v^2`

`(214 (cancel(kg)*m^2)/s^2)/ (0.148cancel( kg)) = v^2`

`1445.95 m^2/s^2 = v^2`

`v = sqrt(1445.95 m^2/s^2) ~~38.03 m/s`