A 70 kg person is riding on a frictionless skateboard at 5 m/s. A friend facing him throws a 5kg ball toward him at 20 m/s. What is his final speed after catch the ball?
70*5 - 5*20 = 75 v
Answer is (10/3)V or 3.333V
To find the person's final speed after catching the ball, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the catch should be equal to the total momentum after the catch.
First, let's find the initial momentum of the person. Momentum is given by the formula:
Momentum = Mass x Velocity
For the person, the mass is 70 kg, and the initial velocity is 5 m/s. Therefore, the initial momentum of the person is:
Initial momentum(person) = 70 kg x 5 m/s = 350 kg m/s (forward)
Next, let's find the initial momentum of the ball. The mass of the ball is 5 kg, and the initial velocity is 20 m/s. Therefore, the initial momentum of the ball is:
Initial momentum(ball) = 5 kg x 20 m/s = 100 kg m/s (toward the person)
Now, let's consider the final momentum. After catching the ball, the person and the ball move together with a common final velocity. Let's assume this final velocity is V (m/s) in the forward direction (since the person was originally moving in the forward direction).
The final momentum of the person and the ball together will be:
Final momentum(person + ball) = (total mass) x (final velocity)
The total mass is the sum of the person's mass and the ball's mass, which is 70 kg + 5 kg = 75 kg.
So, the final momentum equation becomes:
Final momentum(person + ball) = 75 kg x V (forward)
According to the conservation of momentum principle, the initial momentum is equal to the final momentum. Therefore, we can equate the initial momentum of the person and the ball to the final momentum of the person and the ball:
Initial momentum(person) + Initial momentum(ball) = Final momentum(person + ball)
350 kg m/s + 100 kg m/s = 75 kg x V
450 kg m/s = 75 kg x V
To find the final velocity V, we can rearrange the equation:
V = (450 kg m/s) / (75 kg)
V = 6 m/s (forward)
Hence, the person's final speed after catching the ball is 6 m/s in the forward direction.