Question

Shooting a gun from a ship gets the ship into motion. Pick a bullet of 50kg, which is fired at 400m/s. Your vessel has a total mass of 50 tons. Which velocity fo you gain for a single shot? How much for a second shot?

Answer 1

Ans.

mass of bullet m₁  = 50 kg.

velocity of bullet v₁ = 400 m/s.

mass of vessel m₂ = 50 tons = 45359.2 kg.

by conservation of linear momentum

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where u₁ and u₂ are initial velocity and v₁ and v₂ are final velocity of bullet and vessel respectively.

since u₁ and u₂ = 0

m₁v_{1 =} -m₂v₂

v₂ = -m₁v₁ /m₂

v₂ = (50*400)/(45359.2)

v₂ = -0.44 ms^-1.

for second shot u₁ = u₂ =-0.44 ms^-1 and v₁ =400 ms^-1

again using conservation of momentum

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂   

-(50 + 45359.2) * 0.44 =50*400 + 45359.2 * v₂

v₂ = (-19980.04 - 20000)/45359.2

v₂ = -0.88 ms^-1

hence after second shot the velocity gain by the vessel is = -0.88 ms^-1

^{here minus sign indicate that the velocity of vessel is opposite to the velocity of bullet}