Question

The second carriage moves at 0.8 m/s to the right after the collision.

Calculate the velocity after the collision of the first carriage if the collision is perfectly elastic.

A. 0.40 m/s to the left
B. 0.22 m/s to the left
C. 1.34 m/s to the left
D. 3.17 m/s to the left

Answer 1

In an elastic collision, the momentum and kinetic energy are conserved. The velocity of the first carriage after the collision can be found using the equation m1v1 + m2v2 = m1v1' + m2v2', where m1 and m2 are the masses of the carriages, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities. The correct answer is A. 0.40 m/s to the left.

Step-by-step explanation:

In an elastic collision, both the momentum and kinetic energy are conserved. To find the velocity of the first carriage after the collision, we can use the equation:

m1v1 + m2v2 = m1v1' + m2v2'

Where m1 and m2 are the masses of the carriages, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities. Since the second carriage is moving to the right after the collision, its velocity v2' is 0.8 m/s to the right.

Plugging in the given values, we have:

(m1 * 24 m/s) + (m2 * (-12 m/s)) = (m1 * v1') + (m2 * 0.8 m/s)

Solving this equation will give us the velocity v1' of the first carriage after the collision. From the given options, the answer is A. 0.40 m/s to the left.