Question

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Explosion
1) Two swimmers are floating on a raft that is motionless. One swimmer has a mass of 50 kg and
the other at 80 kg. They both push off the raft at the same time. The 80 kg swimmer moves
away at 3 m/s. What velocity does the 50 kg swimmer move away with?
M1 = 50 kg v1' =____ M2 = 80 kg v2' = 3 m/s
Equation: 0= m1 (v1') + m2 (v2')
Elastic
2) Two hockey players are skating towards each other. A 90 kg player traveling at 6 m/s
rams into a 60 kg player moving at 2 m/s. After the collision, the 90 kg player slows to 4
m/s but is still traveling in the same direction. What is the velocity of the 60 kg player?
Equation: m1 (v1) + m2 (v2) = m1 (v1') + m2 (v2')
v2 = -2 m/s
M1 = 90 kg
v1 = 6 m/s M2 = 60 kg
V1' = 4 m/s
v2' =___

Answer 1

We can use the conservation of momentum to solve both problems:

Conservation of momentum:

0 = m1(v1') + m2(v2')

where m1 = 50 kg, v2' = 3 m/s, and m2 = 80 kg. We can solve for v1' to get:

v1' = -(m2/m1) v2'

v1' = -(80 kg/50 kg) (3 m/s) = -4.8 m/s

Therefore, the 50 kg swimmer moves away from the raft with a velocity of -4.8 m/s.

Conservation of momentum:

m1(v1) + m2(v2) = m1(v1') + m2(v2')

where m1 = 90 kg, v1 = 6 m/s, m2 = 60 kg, and v1' = 4 m/s. We can solve for v2 to get:

v2 = (m1v1 + m2v2 - m1v1') / m2

v2 = (90 kg)(6 m/s) + (60 kg)(2 m/s) - (90 kg)(4 m/s) / 60 kg

v2 = -1 m/s

Therefore, the velocity of the 60 kg player after the collision is -1 m/s, which means they are moving in the opposite direction to the 90 kg player.