Question

A father and daughter are riding their bikes at the same speed. The father's mass is three times the daughter's mass.
A side view of a man and child riding bicycles next to each other.
If the father’s kinetic energy is \[300\,\text{J},\] what is the daughter's kinetic energy?

Answer 1

Kinetic energy (KE) is given by the formula:

\[
KE = \frac{1}{2} mv^2
\]

where:
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.

Let us denote the mass of the daughter as \( m_d \) and the mass of the father as \( m_f = 3m_d \) (since the father’s mass is three times the daughter’s mass).

Given that the father’s kinetic energy is \( 300 \, \text{J} \), we can express this using the kinetic energy formula:

\[
KE_f = \frac{1}{2} m_f v^2 = \frac{1}{2} (3m_d) v^2 = \frac{3}{2} m_d v^2
\]

We know \( KE_f = 300 \, \text{J} \), thus:

\[
\frac{3}{2} m_d v^2 = 300
\]

Now, we want to find the daughter’s kinetic energy, \( KE_d \):

\[
KE_d = \frac{1}{2} m_d v^2
\]

To relate \( KE_d \) to \( KE_f \), we can express \( KE_d \) in terms of \( KE_f \):

First, we can solve for \( m_d v^2 \) from the equation for \( KE_f \):

\[
m_d v^2 = \frac{2}{3} \cdot 300
\]

Calculating that gives:

\[
m_d v^2 = 200 \, \text{J}
\]

Now substituting this back into the equation for \( KE_d \):

\[
KE_d = \frac{1}{2} m_d v^2 = \frac{1}{2} \cdot 200 = 100 \, \text{J}
\]

Thus, the daughter’s kinetic energy is:

\[
\boxed{100 \, \text{J}}
\]