Question

1. marcus and caitlin are bowling. both of them released their balls down the 20 m lane at the same time. marcus uses a 6 kg ball, and caitlin uses a 4 kg ball. caitlins ball hits the first pin after 5 seconds, and marcus ball hits the first pin 3 seconds later.

caitlin claims that her ball had more kinetic energy, but marcus claims that his ball does.
which of the following statements is true?
a. marcus ball has more kinetic energy because his balls mass is greater, which has a larger impact on kinetic energy than mass.
b. caitlins ball has more kinetic energy because her balls velocity is greater, which has a larger impact on kinetic energy than mass.
c. marcus ball has less kinetic energy because his balls mass is greater, and mass has an inverse relationship with kinetic energy.
d. caitlins ball has less kinetic energy because her balls velocity is greater, and velocity has an inverse relationship with kinetic energy.

Explanation:

Step1: Calculate velocities

Velocity formula \(v=\frac{d}{t}\).
For Caitlin: \(d = 20m\), \(t = 5s\), so \(v_{C}=\frac{20}{5}=4m/s\).
For Marcus: \(t=(5 + 3)s=8s\), \(v_{M}=\frac{20}{8}=2.5m/s\).

Step2: Calculate kinetic energies

Kinetic energy formula \(K.E.=\frac{1}{2}mv^{2}\).
For Caitlin: \(m = 4kg\), \(v = 4m/s\), \(K.E._{C}=\frac{1}{2}\times4\times4^{2}=32J\).
For Marcus: \(m = 6kg\), \(v = 2.5m/s\), \(K.E._{M}=\frac{1}{2}\times6\times2.5^{2}=18.75J\).
Also, since \(K.E.=\frac{1}{2}mv^{2}\), velocity is squared, so it has a larger impact on \(K.E.\) than mass.

Answer:

B. Caitlin's ball has more kinetic energy because her ball's velocity is greater, which has a larger impact on kinetic energy than mass.