Question

A 28.0-g object moving to the right at 20.5 cm/s overtakes and collides elastically with a 11.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. (Take the positive direction to be to the right. Indicate the direction with the sign of your answer.)

Answer 1

After an elastic collision between two objects of equal mass, with one object moving initially in the +x-direction and the other object moving initially in the -x-direction, the velocity of the second object after the collision can be calculated using the principle of conservation of momentum. In this case, the velocity of object A after the collision is given as 8.0 m/s in the -x-direction. To find the velocity of object B after the collision, we can set up an equation and solve for it. The velocity of object B after the collision is 4.0 m/s in the -x-direction.

Step-by-step explanation:

Given that two objects, A and B, with equal mass collide elastically, we can use the principle of conservation of momentum to determine the velocity of object B after the collision. Before the collision, object A is moving at 4.0 m/s in the +x-direction, and object B is moving at 8.0 m/s in the -x-direction. After the collision, object A moves with a velocity of 8.0 m/s in the -x-direction.

To find the velocity of object B after the collision, we can set up the equation:

(mass of A)(velocity of A before) + (mass of B)(velocity of B before) = (mass of A)(velocity of A after) + (mass of B)(velocity of B after)

Plugging in the given values:

(1)(4.0) + (1)(8.0) = (1)(8.0) + (1)(velocity of B after)

Simplifying the equation:

4 + 8 = 8 + velocity of B after

12 = 8 + velocity of B after

Subtracting 8 from both sides:

velocity of B after = 12 - 8 = 4.0 m/s in the -x-direction.