Question

A 0.159 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.820 m/s. It has a head-on collision with a 0.301 kg glider that is moving to the left with a speed of 2.14 m/s. Suppose the collision is elastic.

Find the magnitude of the final velocity of the 0.159 kg glider.

Find the direction of the final velocity of the 0.159 kg glider.

Find the magnitude of the final velocity of the 0.301 kg glider.

Find the direction of the final velocity of the 0.301 kg glider.

Answer 1

here,

the mass of first glider , m1 = 0.159 kg

mass of second glider , m2 = 0.301 kg

the initial speed of 1 , u1 = 0.82 m/s

let the final velocity of gliders be v1 and v2

using conservation of momentum

m1 * u1 = m1 * v1 + m2 * v2

0.159 * 0.82 = 0.159 * v1 + 0.301 * v2 ....(1)

and

using conservation of kinetic energy

0.5 * m1 * u1^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

0.159 * 0.82^2 = 0.159 * v1^2 + 0.301 * v2^2
....(2)

from (1) and (2)

v1 = - 0.25 m/s

v2 = 0.57 m/s

the magnitude of the final velocity of the 0.159 kg glider is 0.25 m/s

the direction of the final velocity of the 0.159 kg glider is in opposite direction to the initial direction of motion

the magnitude of the final velocity of the 0.301 kg glider is 0.57 m/s

the direction of the final velocity of the 0.301 kg glider in the same initial direction