Question

Two objects collide head on. Assume they have equal masses but unequal velocities, such that the one coming in from the right is moving at 23.92 m/s toward the left, and the one coming in from the left is moving at 86.56 m/s toward the right. After the collision, what is the velocity of the one that came in from the left? (Use + to the right and - to the left to distinguish direction in your answer.) Give your answer in m/s.

Answer 1

here,

the masses of each is m

the initial velocity of 1 , u1 = - 23.92 m/s

the initial velocity of 2 , u2 = 86.56 m/s

let the final velocities after the collison be v1 and v2

using conservation of momentum

m *u1 + m * u2 = m * v1 + m * v2

- 23.92 + 85.56 = v1 + v2 ....(1)

and

using conservation of kientic energy

0.5 * m *u1^2 + 0.5 * m * u2^2 = 0.5 * m * v1^2 + 0.5 * m * v2^2

23.92^2 + 85.56^2 = v1^2 + v2^2 ....(2)

from (1) and (2)

v2 = - 23.92 m/s

v1 = 85.56 m/s

the velocity of the one that came in from the left is 85.56 m/s to the left