Question

8. A 50.0 kg woman, riding on a 10 kg cart, is moving east at 5.0 m/s. The woman jumps off the front of the cart and lands on the ground at 7.0 m/s eastward. What is the final velocity of the cart

Answer 1

To find the final velocity of the cart, we can use the conservation of momentum principle. Momentum is defined as mass times velocity, and in an isolated system, the total momentum before an event equals the total momentum after the event.

Before the woman jumps off the cart, the total momentum of the system is (50 kg)(5 m/s) = 250 kg m/s. After the woman jumps off, the total momentum of the cart is (10 kg)(v), where v is the final velocity of the cart.

Using the conservation of momentum principle, we can write the following equation:

(50 kg)(5 m/s) = (10 kg)(v) + (50 kg)(7 m/s)

Solving for v, we get:

v = (250 kg m/s - (50 kg)(7 m/s)) / 10 kg

v = -25/10

v = -2.5 m/s

So the final velocity of the cart is -2.5 m/s (westward direction)