Question

A 30g bullet is fired from a 1.6 kg rifle at a target. If the muzzle velocity of the bullet is 360 m/s what is the recoil velocity of the rifle?

Answer 1

Approximately
`6.75\; {\rm m\cdot s^(-1)}`.

Step-by-step explanation:

Let
`u` denote the initial velocity and let
`v` denote the velocity after launching.

By the conservation of momentum, the sum of momentum would the same before and after launching:

`m_(b)\, u_(b) + m_(r) \, u_(r) = m_(b)\, v_(b) + m_(r)\, v_(r)`.

Assuming that
`u_(b) = u_(r) = 0\; {\rm m\cdot s^(-1)}`:

`m_(b)\, v_(b) + m_(r)\, v_(r) = 0`.

It is given that
`v_(b) = 360\; {\rm m\cdot s^(-1)}` and
`m_(r) = 1.6\; {\rm kg}`. Apply unit conversion and ensure that mass values are measured in the same unit (kilograms):

`m_(b) = 30\; {\rm g} = 30 * 10^(-3)\; {\rm kg} = 0.030\; {\rm kg}`.

Substitute these values into the equation and solve for
`v_(r)`:

`\begin{aligned}v_(r) &= (-m_(b)\, v_(b))/(m_(r))\\ &= \frac{-(0.030\; {\rm kg})\, (360\; {\rm m\cdot s^(-1)})}{1.6\; {\rm kg}} \\ &= 6.75\; {\rm m\cdot s^(-1)}\end{aligned}`.