Answer :
ANSWER
80 m/s
EXPLANATION
Given:
• Bullet's mass: 1kg
,• Gun's mass: 5kg
,• Bullet's final speed: 400m/s
Unknown:
• Gun's final speed
In this motion, momentum is conserved. Both initial speeds are zero because we can assume that before firing the gun and bullet are at rest. Thus, the momentum equation is,
[tex]m_b\cdot v_b+m_g\cdot v_g=0[/tex]Solving for vg,
[tex]v_g=\frac{-m_b\cdot v_b}{m_g_{}}[/tex]It is negative because its direction is opposite to the direction of the bullet's speed,
[tex]v_g=\frac{-1kg\cdot400m/s}{5\operatorname{kg}}=-80m/s[/tex]The recoil speed is 80m/s