I am very confused about this problem:
A ball hits a car going 50 miles per hour. What is the incident velocity of the ball to have v=0 after the impact?
To find the incident velocity of the ball that would make its velocity zero after the impact with the car, we need to use the principle of conservation of momentum. The total momentum before the collision will be equal to the total momentum after the collision.
Let's assume the mass of the ball is "m" and the mass of the car is "M". The velocity of the car before the impact is given as 50 miles per hour (50 mph) or 22.352 meters per second (m/s). We need to find the incident velocity of the ball, let's call it "V".
The momentum before the collision is given by:
Momentum before = momentum of the ball + momentum of the car
The momentum of an object is given by its mass multiplied by its velocity:
Momentum = mass × velocity
So, the momentum before the collision is:
(Mass of the ball × Incident velocity) + (Mass of the car × Velocity of the car before the impact)
The momentum after the collision should be zero because the ball comes to rest. So, we can write:
Momentum after = 0
Now, equating the momentum before and after the collision, we get:
(M × V) + (m × 0) = 0
Since the mass of the ball is not zero (m ≠ 0), we can ignore the second term on the left side of the equation. Therefore, we have:
M × V = 0
Dividing both sides by M, we find:
V = 0
Hence, the incident velocity of the ball needs to be zero for it to have zero velocity after the collision.
In other words, if the ball hits the car when it is already at rest (incident velocity = 0), the ball's velocity will become zero after the impact.