Question

A hunter (mass m₁) sits in a boat (mass m₂=  2m₁) which can move in the water without resistance. The boat is initially at rest. a) Determine the velocity v_B1 of the boat after the hunter fires a bullet (mass m₃ = m₁/1000) with a velocity v₀ = 500 m/s. b) Find the direction of the velocity of the boat after a second shot is fired at an angle of 45^◦ with respect to the first one.

Answer 1

a) We introduce a coordinate system and assume that the bullet is fired in the direction of the negative x-axis. Since the linear momentum before the firing of the bullet is zero, the total linear momentum of the system after the firing (velocities positive to the right) also has to be zero:

The algebraic sign shows that the boat moves in the direction of the positive x-axis. 

b) Now, we have to formulate the Impulse Laws in the x- and y-direction

They lead to