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Answer :
Final answer:
Using the conservation of momentum, the speed and direction of the canoe and the remaining camper are determined to be 2.43 m/s backwards after the other camper leaves the canoe moving forward at 3.7 m/s.
Explanation:
The question deals with the conservation of momentum, a concept in physics where the total momentum of a closed system is constant if no external forces act on it. When one camper leaves the canoe moving forward with a certain velocity, the canoe and the remaining camper move in the opposite direction to conserve momentum. To find the speed and direction in which the canoe and the remaining camper move, we use the equation:
p_initial = p_final
where p stands for momentum. Momentum, p, is the product of mass, m, and velocity, v:
- p = m * v.
For the intial scenario, the canoe is stationary, so p_initial = 0. When the camper steps onto the dock, she moves with a momentum p_camper = m_camper * v_camper = 75.0 kg * 3.7 m/s. Hence, the canoe and the other camper must have the same momentum in the opposite direction to conserve the total momentum:
p_canoe = m_canoe * v_canoe = - p_camper
v_canoe = - (m_camper * v_camper) / m_canoe
Substituting the values:
v_canoe = - (75.0 kg * 3.7 m/s) / 115 kg
= -2.43 m/s
The negative sign indicates the direction is opposite to the direction the camper moved, which means the canoe and the other camper move backwards at 2.43 m/s.
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