To calculate the velocities of the balls after an elastic collision, you can use the conservation of momentum and kinetic energy equations. Solve the equations using the given masses and initial velocities to find the final velocities of the balls.
In this scenario, the context is that kids are facing each other and playing with playground balls, which collide elastically. The exigence, or the reason for asking the question, is to determine the velocities of the balls after they collide.
In an elastic collision, the total kinetic energy and momentum of the system are conserved. Therefore, to calculate the velocities of the balls after the collision, you need to know their initial velocities and masses.
You can use the conservation of momentum and kinetic energy equations to solve for the unknown velocities. Let's assume that ball A has a mass of mA and an initial velocity of
ball B has a mass of
and an initial velocity of
After the collision, ball A has a final velocity of v'ₐ, and ball B has a final velocity of v'ₐ. The conservation equations are:
- Momentum: mA *
B *
mA * v'ₐ +
v'ₐ - Kinetic Energy: 1/2 * mA * vA² + 1/2 *
B² = 1/2 * mA * v'ₐ² + 1/2 *
'ₐ²
Solving these equations will provide you with the final velocities of the balls after the collision.