A 16.0 kg canoe moving to the left at -12.5 m/s makes an elastic head on collision with a 14.0 raft moving
to the right at 16.0 m/s. After the collision the raft moves to the left at -14.4 m/s. Assuming water simulates
a frictionless surface, what is the velocity of the canoe after the collision?
When I did the problem, I got a velocity of 14.1 m/s.
To solve this problem, we can apply the principles of conservation of momentum and apply the law of conservation of kinetic energy.
The law of conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant.
The equation for conservation of momentum is:
m1*v1(initial) + m2*v2(initial) = m1*v1(final) + m2*v2(final)
We are given the following values:
m1 (mass of the canoe) = 16.0 kg
v1(initial) (initial velocity of the canoe) = -12.5 m/s
m2 (mass of the raft) = 14.0 kg
v2(initial) (initial velocity of the raft) = 16.0 m/s
v2(final) (final velocity of the raft) = -14.4 m/s
Let's solve the equation for conservation of momentum to find the final velocity of the canoe:
16.0 kg * (-12.5 m/s) + 14.0 kg * (16.0 m/s) = 16.0 kg * v1(final) + 14.0 kg * (-14.4 m/s)
Using this equation, we can solve for v1(final) to find the velocity of the canoe after the collision.