Question

A knife thrower throws a knife toward a 300 g target that is sliding in her direction at a speed of 2.30 m/s on a horizontal frictionless surface. She throws a 22.5 g knife at the target with a speed of 40.0 m/s. The target is stopped by the impact and the knife passes through the target. Determine the speed of the knife (in m/s) after passing through the target.

Answer 1

Answer:

The speed of the knife after passing through the target is 9.33 m/s.

Explanation:

We can find the speed of the knife after the impact by conservation of linear momentum:

$p_{i} = p_{f}$

$m_{k}v_{i_{k}} + m_{t}v_{i_{t}} = m_{k}v_{f_{k}} + m_{t}v_{f_{t}}$

Where:

$m_{k}$: is the mass of the knife = 22.5 g = 0.0225 kg

$m_{t}$: is the mass of the target = 300 g = 0.300 kg

$v_{i_{k}}$: is the initial speed of the knife = 40.0 m/s

$v_{i_{t}}$: is the initial speed of the target = 2.30 m/s

$v_{f_{k}}$: is the final speed of the knife =?

$v_{f_{t}}$: is the final speed of the target = 0 (it is stopped)

Taking as a positive direction the direction of the knife movement, we have:

$m_{k}v_{i_{k}} - m_{t}v_{i_{t}} = m_{k}v_{f_{k}}$  

$v_{f_{k}} = \frac{m_{k}v_{i_{k}} - m_{t}v_{i_{t}}}{m_{k}} = \frac{0.0225 kg*40.0 m/s - 0.300 kg*2.30 m/s}{0.0225 kg} = 9.33 m/s$

Therefore, the speed of the knife after passing through the target is 9.33 m/s.

I hope it helps you!