Question

a mother throws a bowling ball, giving it 180 j of kinetic energy. then, her son throws his bowling ball at the same speed. his ball has one-half the mass of the mother’s ball. how much kinetic energy did the son give his bowling ball?

Explanation:

Step1: Recall the kinetic energy formula

The formula for kinetic energy is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is speed.

Step2: Define variables for mother's ball

Let the mass of the mother's ball be $m_m$ and speed be $v$. So her kinetic energy $KE_m=\frac{1}{2}m_mv^2 = 180\space J$.

Step3: Define variables for son's ball

The son's ball has mass $m_s=\frac{1}{2}m_m$ and speed $v$ (same as mother's). His kinetic energy $KE_s=\frac{1}{2}m_sv^2$.

Step4: Substitute $m_s$ into son's KE formula

Substitute $m_s=\frac{1}{2}m_m$ into $KE_s$: $KE_s=\frac{1}{2}(\frac{1}{2}m_m)v^2=\frac{1}{2}(\frac{1}{2}m_mv^2)$.

Step5: Relate to mother's KE

We know $\frac{1}{2}m_mv^2 = KE_m = 180\space J$, so $KE_s=\frac{1}{2}\times180\space J$.

Step6: Calculate son's KE

$\frac{1}{2}\times180 = 90\space J$.

Answer:

90 J