Question

A certain 8lb hunting rifle fires a 180 grain bullet at a target 1000yds away. The bullet experiences an acceleration of ?2.7 m s 2 (opposite direction of velocity) due to air resistance. When the bullet hits the target, its velocity is measured to be 820 m s . Express all answers in SI units. Helpful conversions:

1 grain = 6.48

Answer 1

A shell (i.e. bullet) of mass, Mb = 10kg is fired from a gun of mass, Mg = 600kg. The gun recoils with a velocity, Vg of 6m/s, then the mass of the bullet is....
In Newton's 3rd Law of motion,

The gun has a momentum of m * v, using the gun's mass and velocity.
The bullet has a momentum of m * v, using the bullet's mass and velocity (make them capital letters or give them a subscript or something to distinguish from the gun).

The momentums are equal and opposite. Set those equal, plug in the three things you know and solve for the fourth thing you are being asked for.

consider the recoil of a gun, where the backward momentum is equal to the forward momentum, i.e.
Backward Momentum = Forward Momentum ? MgVg = MbVb, then by substitution, you'll have
600kg * 6m/s = 10kg * Vb
3,600kgm/s = 10kg * Vb
=> Divide both sides by 10kg, then finally,
Vb, which is the velocity of the bullet (i.e. shell) = 360m/s ...Ans.