A 0.144 kg glider is moving to the right on a frictionless, horizontal air track

Question

A 0.144 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.740 m/s . It has a head-on collision with a 0.291 kg glider that is moving to the left with a speed of 2.21 m/s. Suppose the collision is elastic

A) Find the magnitude of the final velocity of the 0.144 kg glider.

B) Find the direction of the final velocity of the 0.144 kg glider.

C)Find the magnitude of the final velocity of the 0.291 kg glider.

D)Find the direction of the final velocity of the 0.291 kg glider.

Explanation / Answer

given,

mass of first glider m1 = 0.144 kg

mass of second glider m2 = 0.291 kg

speed of first glider = 0.74 m/s

speed of second glider = 2.21 m/s

initial momentum = m1 * v1 + m2 * v2

initial momentum = 0.144 * 0.74 - 0.291 * 2.21

final momentum = m1 * v3 + m2 * v4

by conservation of momentum

initial momentum = final momentum

0.144 * 0.74 - 0.291 * 2.21 = 0.144 * v3 + 0.291 * v4

by conservation of energy

initial energy = final energy

0.5 * 0.144 * 0.74^2 + 0.5 * 0.291 * 2.21^2 = 0.5 * 0.144 * v3^2 + 0.5 * 0.291 * v4^2

on solving we'll get

v3 = -3.2 m/s

v4 = -0.257 m/s

magnitude of the final velocity of the 0.144 kg glide = 3.2 m/s

direction of the final velocity of the 0.144 kg glider is toward left

magnitude of the final velocity of the 0.291 kg glider = 0.257 m/s

direction of the final velocity of the 0.291 kg glider is toward left

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