Question

A baggage cart full of luggage is coasting at a speed vA across the airport taxiway. When fifty-nine percent of the mass of the cart and luggage is thrown off the cart, parallel to the ground and in the forward direction, the cart is brought to a halt. If the direction in which this mass is thrown is exactly reversed, but the speed of this mass relative to the cart remains the same, the cart accelerates to a new speed vB. Calculate the ratio vB/vA.

Answer 1

To find the ratio vB/vA, we can use the conservation of momentum and calculate the initial and final momenta.

Step-by-step explanation:

In this problem, we have a baggage cart full of luggage coasting at a speed vA across the airport taxiway. When 59% of the mass of the cart and luggage is thrown off the cart in the forward direction, the cart comes to a halt.

If we reverse the direction in which this mass is thrown, but keep the speed relative to the cart the same, the cart accelerates to a new speed vB. We need to calculate the ratio vB/vA.

Let's denote the initial mass of the cart and luggage as M, and the initial velocity of the cart as vA. After 59% of the mass is thrown off, the remaining mass is 0.41M, and the velocity of the cart becomes 0 m/s. This means that the change in momentum is equal to the initial momentum. Using the conservation of momentum, we can calculate the initial momentum and the final momentum, and therefore find the ratio vB/vA.