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Two hard, steel carts collide head-on and then ricochet off each other in opposite directions on a frictionless surface. Cart A has a mass of 0.350 kg and an initial velocity of 2 m/s. Cart B has a mass of 0.500 kg and an initial velocity of −0.500 m/s. After the collision, cart A recoils with a velocity of −4 m/s. What is the final velocity of cart B?

Question

Two hard, steel carts collide head-on and then ricochet off each other in opposite directions on a frictionless surface. Cart A has a mass of 0.350 kg and an initial velocity of 2 m/s. Cart B has a mass of 0.500 kg and an initial velocity of −0.500 m/s. After the collision, cart A recoils with a velocity of −4 m/s. What is the final velocity of cart B?

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Solution

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is given by the product of its mass and velocity.

Step 1: Calculate the initial momentum of each cart.

For cart A: Initial momentum = mass * velocity = 0.350 kg * 2 m/s = 0.7 kg*m/s

For cart B: Initial momentum = mass * velocity = 0.500 kg * -0.500 m/s = -0.25 kg*m/s

Step 2: Calculate the total initial momentum.

Total initial momentum = momentum of A + momentum of B = 0.7 kgm/s - 0.25 kgm/s = 0.45 kg*m/s

Step 3: Calculate the final momentum of cart A.

Final momentum of A = mass * final velocity = 0.350 kg * -4 m/s = -1.4 kg*m/s

Step 4: Use the conservation of momentum to find the final momentum of cart B.

Total final momentum = final momentum of A + final momentum of B

So, final momentum of B = total initial momentum - final momentum of A = 0.45 kgm/s - (-1.4 kgm/s) = 1.85 kg*m/s

Step 5: Calculate the final velocity of cart B.

Final velocity of B = final momentum of B / mass of B = 1.85 kg*m/s / 0.500 kg = 3.7 m/s

So, the final velocity of cart B is 3.7 m/s.

This problem has been solved

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