Question

For the preceding problem, find the final speed of each sled for the case of an elastic collision.

Reference Problem:
A child sleds down a hill and collides at 5.6 m/s into a stationary sled that is identical to his. The child is launched forward at the same speed, leaving behind the two sleds that lock together and slide forward more slowly. What is the speed of the two sleds after this collision?

a) 5.6 m/s, 0 m/s
b) 2.8 m/s, 2.8 m/s
c) 0 m/s, 5.6 m/s
d) 4.2 m/s, 4.2 m/s

Answer 1

In an elastic collision between two identical sleds, the final speed of each sled can be calculated by applying the principle of conservation of momentum. The correct option is b) 2.8 m/s, 2.8 m/s.

Step-by-step explanation:

In an elastic collision, both momentum and kinetic energy are conserved. For the case of an elastic collision between two identical sleds, if one sled is initially at rest and the other sled is moving with a speed of 5.6 m/s, the final speed of each sled can be calculated using the principle of conservation of momentum.

Let's assume the final speed of the two sleds together is Vf. Applying the principle of conservation of momentum:

(mass of sled 1) * (final speed of sled 1) + (mass of sled 2) * (final speed of sled 2) = (mass of sled 1 + mass of sled 2) * (final speed of the two sleds)

Since the sleds are identical and have the same mass, we can rewrite this equation as:

2 * (final speed of sled) = (2 * (mass of sled)) * (final speed of the two sleds)

Given that the initial speed of one sled is 5.6 m/s and the final speed of both sleds is the same, the final speed of each sled is 2.8 m/s. So, the correct option is b) 2.8 m/s, 2.8 m/s.