Question

If a 35 g arrow moving at 160 km/h penetrates a block of wood suspended by a rope, what impulse is delivered to the block? (Answer: 1.56kg * m/s)

What velocity will the wood block acquire if its mass is 7.0 kg? Ignore the mass of the arrow compared to that of the wood block. (Answer: 0.222m/s)

Please show all work on how to get those answers.

Answer 1

To the first problem, you need to convert all the numbers to the correct units.

35 kg = 0.035 kg
160 km/h = 44.44 m/s (Hint: to convert km/h quickly to m/s, divide by 3.6)

So, it is asking for the impulse which is

Imp = mv
Imp = (0.035 kg)(44.44 m/s) = 1.56 kg-m/s

To the second problem, you are trying to find the velocity assuming the impulse is the same.

v = p/m
v = (1.56 kg-m/s) / (7.0 kg) = 0.222 m/s