Question

Esteban hits a 0.145kg baseball traveling at him at +27.0m/s. the ball is in contact with the bat for 0.133 seconds with an average force of 51.2n. cakculate the final velocity of the baseball.m=u-u=f=v=

Answer 1

In order to calculate the final velocity of the ball, first let's calculate the initial momentum:

$\begin{gathered} p=mv\\ \\ p=0.145\cdot27\\ \\ p=3.915\text{ kg m/s} \end{gathered}$

Now, using the impulse theorem, let's calculate the change in momentum:

$\begin{gathered} \Delta p=I\\ \\ \Delta p=F\cdot\Delta t\\ \\ \Delta p=51.2\cdot0.133\\ \\ \Delta p=6.8096\text{ kg m/s} \end{gathered}$

Adding the change in momentum to the initial momentum, we can find the final momentum:

$\begin{gathered} p_f=p+\Delta p\\ \\ p_f=3.915+6.8096\\ \\ p_f=10.7246\text{ kg m/s} \end{gathered}$

Using the final momentum, let's calculate the final velocity:

$\begin{gathered} p=mv\\ \\ 10.7246=0.145\operatorname{\cdot}v\\ \\ v=\frac{10.7246}{0.145}\\ \\ v=73.96\text{ m/s} \end{gathered}$