A bullet weighing 20 g, flying at a speed of 700 m / s at an angle of 60 ° to the horizon, hits a 4 kg bag

A bullet weighing 20 g, flying at a speed of 700 m / s at an angle of 60 ° to the horizon, hits a 4 kg bag of sand lying on a smooth horizontal table and gets stuck in it. Determine the speed at which the bag slides across the table.

Let us write the equation of the law of conservation of momentum in projection onto the horizontal axis:

mV1 cos α = (m + M) VС,

where m is the mass of the bullet, m = 20 g; V1 – bullet speed, V1 = 700 m / s; α – angle, α = 60о; M is the mass of the sand bag, M = 4 kg; VС – speed of sliding of a bag with a bullet on a horizontal table.

Seeking speed VС:

VС = mV1 cos α / (m + M).

Substitute the numerical values in SI units:

VС = 0.02 × 700 × cos (60о) / (0.02 + 4) = 1.741 m / s.

Answer: 1.741 m / s.