Question

A 10.2kg rifle fires a 60g bullet horizontally at a 2kg block of wood 200m away. The bullet collides inelastically and lifts the block 1.2m high.

A.) what is the speed of the block and the bullet right after impact?

B.) What was the speed of the bullet right before impact?

C.) what was the speed of the bullet as it left the muzzle of the rifle

D.)what is the recoil on the rifle

Answer 1

here,

mass of rifle , m1 = 10.2 kg

mass of bullet , m2 = 60 g = 0.06 kg

mass of block , m3 = 2 kg

A)

h = 1.2 m

the speed of the block and the bullet right after impact , v = sqrt(2 * g * h)

v = sqrt(2*9.81*1.2) = 4.85 m/s

B)

let the speed of the bullet right before impact be u

using conservation of momentum

m2 * u = (m2 + m3) * v

0.06 * u = ( 0.06 + 2) * 4.85

u = 166.6 m/s

C)

the speed of the bullet as it left the muzzle of the rifle is 166.6 m/s

D)

let the recoil on the rifle be v0

using conservation of momentum for rifle-bullet system

m1 * v0 = m2 * u

10.2 * v0 = 0.06 * 166.6

v0 = 0.98 m/s