Question

A white ball traveling at 2.0 m/s hits an equal mass red ball at rest. The white ball is deflected by 25∘and slowed to 1.5 m/s. What is the magnitude of the velocity of the red ball after collision? Express your answer with the appropriate units.

Answer 1

To find the magnitude of the velocity of the red ball after collision, we can use the principles of conservation of momentum and kinetic energy. First, calculate the initial kinetic energy of the white ball. Then, calculate the kinetic energy of the red ball after the collision. Finally, use the equation for final velocity to find the magnitude of the red ball's velocity after collision.

Step-by-step explanation:

To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy. We know that the white ball hits the red ball, transferring some of its momentum and kinetic energy to the red ball. Since both balls have equal mass, we can assume that half of the initial kinetic energy is transferred to the red ball.

First, we calculate the initial kinetic energy of the white ball:

Kinetic energy (initial) = (1/2) * mass * velocity^2

= (1/2) * 0.25 kg * (2.0 m/s)^2

= 0.25 J

Now, we calculate the kinetic energy of the red ball after the collision:

Kinetic energy (final) = (1/2) * mass * velocity^2

= (1/2) * 0.25 kg * (1.5 m/s)^2

= 0.1875 J

Since the red ball initially had zero velocity, its final velocity can be found using the equation:

Final velocity = sqrt(2 * kinetic energy (final) / mass)

= sqrt(2 * 0.1875 J / 0.25 kg)

= 1.22 m/s

Therefore, the magnitude of the velocity of the red ball after the collision is 1.22 m/s.