a 65kg student holding a 5 kg ball is at rest on ice. if the student throws the ball at 3m/s to the left, what is her velocity after throwing the ball
To find the student's velocity after throwing the ball, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before throwing the ball is equal to the total momentum after throwing the ball.
The momentum of an object is given by the product of its mass and velocity. In this case, the student and the ball are the objects.
Before throwing the ball:
- The mass of the student is 65 kg.
- The mass of the ball is 5 kg.
- The velocity of the student is 0 m/s since they are at rest.
- The velocity of the ball is 0 m/s initially since it is held by the student.
The total momentum before throwing the ball is:
(65 kg) * (0 m/s) + (5 kg) * (0 m/s) = 0 kg*m/s
After throwing the ball:
- The mass of the student remains the same, 65 kg.
- The mass of the ball remains the same, 5 kg.
- The velocity of the student changes after throwing the ball.
- The velocity of the ball changes after being thrown.
Let's assume the student's velocity after throwing the ball is V m/s to the left. The velocity of the ball after being thrown is 3 m/s to the left.
The total momentum after throwing the ball is:
(65 kg) * (V m/s) + (5 kg) * (3 m/s) = 0 kg*m/s
Now, we can solve for V by setting the total momentum before and after the ball is thrown equal to each other:
0 kg*m/s = (65 kg) * (V m/s) + (5 kg) * (3 m/s)
0 kg*m/s = 65V + 15
65V = -15
V = -15 / 65
V ≈ -0.231 m/s
Therefore, the velocity of the student after throwing the ball is approximately -0.231 m/s to the left.