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MCAT Physics Question — Ice Skaters

A motionless, inexperienced ice skater of 70kg faces forward with skates parallel. A more experienced skater of 80kg collides with the stationary skater at a speed of 2m/sec.Both skaters move off together with the same velocity. If ice is considered frictionless, what is the approximate speed of the two skaters after the collision?

a) 1.1m/sec

b) 1.4 m/sec

c) 2 m/sec

d) 4 m/sec


When two masses collide and move with the same velocity after impact, conservation of momentum must be applied. m1v1+m2v2=(m1+m2)vfinal, where v1and v2 are the initial velocities of masses 1 and 2. Here, skater 1 has mass of 70kg and initial velocity of 0m/sec. Skater 2 has a mass of 80kg and initial velocity of 2m/sec.

Applying conservation of momentum, vfinal=m2/( m1+m2)*v2. From looking at the numbers, vfinal is approximately 1/2 of v2 because the skaters have roughly the same mass. Choice a is correct.

a) 1.1m/sec, correct.

b) 1.4 m/sec, incorrect, This assumes kinetic energy before and after is equal. Energy is not conserved in an inelastic collision.

c) 2 m/sec, incorrect, This assumes that speed stays constant after a collision.

d) 4 m/sec, incorrect, This is the initial velocity of the experienced skater squared.

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