Playing in the street, a child accidentally tosses a ball at 21 m/s toward the front of a car moving toward him at 18 m/s. What is the ball's speed after it rebounds elastically from the car?
in the frame of the car, the ball comes in with 39 m/s speed, and bounces back at 39 m/s in the other direction. In the observer frame we need to add the 18 m/s relative speed of the car, and get 57 m/s
57m/s
Well, if the ball is playing in the street, it sounds like it needs a timeout! But let's focus on the physics. Since the collision is elastic, we can use the conservation of momentum.
The initial momentum of the ball is given by its mass (let's call it m) multiplied by its initial velocity (21 m/s). The momentum of the car is given by its mass (let's call it M) multiplied by its velocity (18 m/s).
After the ball bounces off the car, its final momentum will be the same as its initial momentum, just in the opposite direction. So we have:
m * v = -m * v_ball + M * v_car
where v_ball is the ball's final velocity and v_car is the car's final velocity.
Now, since the collision is elastic, kinetic energy is conserved as well. So we also have:
(1/2) * m * v^2 = (1/2) * m * v_ball^2 + (1/2) * M * v_car^2
We can solve these two equations simultaneously to find the final velocity of the ball. Good luck crunching those numbers, math magicians!
To find the ball's speed after rebounding elastically from the car, we can use the principle of conservation of kinetic energy.
The conservation of kinetic energy states that the total kinetic energy before an elastic collision is equal to the total kinetic energy after the collision. In this case, we can assume that the initial kinetic energy of the ball is equal to its final kinetic energy after rebounding.
Let's break down the problem step-by-step:
1. The child throws the ball at a speed of 21 m/s towards the front of the car.
2. The car is moving towards the child at a speed of 18 m/s.
3. To find the relative velocity of the ball with respect to the car, we subtract the car's velocity from the ball's velocity: (21 m/s) - (18 m/s) = 3 m/s.
The relative velocity is the velocity at which the ball approaches the car.
4. During the collision, the ball rebounds elastically. This means that both the momentum and the kinetic energy are conserved.
Since the car is much more massive than the ball, we can assume that the car's velocity does not change significantly.
Therefore, the ball's velocity after rebounding will be equal to the original relative velocity (3 m/s) but in the opposite direction.
This gives us a final velocity of -3 m/s (negative sign indicates opposite direction).
Hence, the ball's speed after rebounding elastically from the car is 3 m/s.
In an elastic collision (1/2) m v^2 does not change.
21 m/s