Question

Fiona and her twin sister April are enjoying the bumper cars at an amusement park. Fiona drives her car toward her sisters and the two cars collide. Before the collision, Fiona was moving with a speed of 3 m/s and April was moving with a speed of 1 m/s. After the collision, Fiona is moving with a speed of 1 m/s and April is moving with a speed of 3 m/s. If Fiona and her bumper car have a combined mass of 80 kg, what is the combined mass of April and her bumper car?
M2 = ? kg

Answer 1

The mass of April and her bumper car is 80 kg

Explanation:

This problem can be solved by using the law of conservation of momentum.

In fact, the total momentum of the system must be conserved before and after the collision, so we have:

$p_i = p_f\\m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$

where:

$m_1 = 80 kg$ is the mass of Fiona+her bumper

$u_1 = 3 m/s$ is the initial velocity of Fiona (we take her direction as positive direction)

$v_1 = -1 m/s$ is the final velocity of Fiona (she rebounds back)

$m_2$ is the mass of April+her bumper

$u_2 = - 1 m/s$ is the initial velocity of April (in the opposite direction)

$v_2 = 3 m/s$ is the final velocity of April

Re-arranging the equation, we can find the mass of April+bumper:

$m_2 = \frac{m_1 u_1 - m_1 v_1}{v_2-u_2}=\frac{(80)(3)-(80)(-1)}{3-(-1)}=80 kg$

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