Question

A bullet of mass 50 g is horizontally fired with a velocity 150 m/s from a pistol of mass 2 kg. What is the recoil velocity of the pistol?​

Answer 1

Answer:

Given:

Mass of bullet =50g = 0.05kg

Velocity of bullet =200m/s

Mass of pistol = 3.5 kg

To Find:

Recoil velocity

Formula:

mass of bullet ×velocity of bullet =mass of

gun×recoil velocity

let mass of bullet be m1 and velocity of bullet be v1

let mass of pistol be m2 and recoil velocity be R

\boxed{\boxed{\mathbb{m1 × v1 = m2 × R}}}m1×v1=m2×R

Solution:

m1 ×v1 = m2 × R

=> 0.05 ×200 = 3.5 × R

=> 10 =3.5R

=> 3.5R = 10

=> R = 10/3.5

=> R = 2.85 m/s

Answer 2

Answer:

Mass of bullet (m1) = 50g = 50/1000 = 0.05 kg

Mass of pistol (m2) = 2kg

Since both are at rest until fired,

Initial velocity (u) = 0 (for pistol and bullet both)

Final velocity of bullet (v1) = 150 m/s

Final velocity of pistol be v

Formula :-

$m1u1 + m2u2 = m1v1 + m2v$

0.05 x 0 + 2 x 0 = 0.05 x 150 + 2 x v

0 = 7.5 + 2v

-7.5 = 2v

v = -7.5/2 = -3.75

Hence the recoil velocity of the pistol is -3.75 m/s