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 determine the student's velocity after throwing the ball, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided there are no external forces acting on the system.
Let's break down the problem step by step:
Step 1: Calculate the initial momentum before throwing the ball.
The initial momentum of the student-ball system can be calculated using the formula:
Initial momentum = mass × velocity
The student's mass is 65 kg, and since the student is at rest, their initial velocity is 0 m/s. Therefore, the initial momentum is:
Initial momentum = 65 kg × 0 m/s = 0 kg·m/s
Step 2: Calculate the momentum of the ball after being thrown.
The momentum of the ball after being thrown can be calculated using the formula:
Momentum = mass × velocity
The mass of the ball is 5 kg, and its velocity after being thrown is 3 m/s to the left (negative direction). Thus, the momentum of the ball is:
Momentum of the ball = 5 kg × (-3 m/s) = -15 kg·m/s
Step 3: Calculate the final momentum after throwing the ball.
Since momentum is conserved, the total momentum after throwing the ball should be equal to the initial momentum. So:
Total momentum after = Total momentum before
Final momentum of the student + Final momentum of the ball = Initial momentum
Let's denote the final velocity of the student as Vf:
(65 kg × Vf) + (-15 kg·m/s) = 0 kg·m/s
Rearranging this equation, we have:
65 kg × Vf = 15 kg·m/s
Step 4: Calculate the final velocity of the student after throwing the ball.
To find the final velocity of the student, we divide both sides of the equation by 65 kg:
Vf = 15 kg·m/s / 65 kg
Vf ≈ 0.231 m/s
Therefore, the student's velocity after throwing the ball is approximately 0.231 m/s to the right.