Question

a 0.25 kg arrow is moving at 5 m/s and hits a 0.10 kg apple. The apple sticks to the arrow, and both move to the right together. What is their velocity?

Answer 1

Answer:

The arrow-apple combo will move with a velocity 3.6 m/s to the right.

Explanation:

Use the law of conservation of momentum to solve this problem. In this case the law can be written as follows:

$m_{arrow}v_{arrow}+m_{apple}\cdot 0= (m_{arrow}+m_{apple})v_{both}$

from which the desired velocity can be isolated:

$\frac{m_{arrow}v_{arrow}}{m_{arrow}+m_{apple}}= v_{both}\\v_{both} = \frac{0.25kg\cdot 5\frac{m}{s}}{0.35kg}=3.6\frac{m}{s}$

The arrow-apple combo will move with a velocity 3.6 m/s to the right.