A bullet with a mass of 10 g flying horizontally at a speed of 50 m / s falls into a box of sand weighing 50 kg

A bullet with a mass of 10 g flying horizontally at a speed of 50 m / s falls into a box of sand weighing 50 kg suspended on a rope and gets stuck in it. To what height does the box rise when deviating after being hit by a bullet?

Bullet kinetic energy:

E = mV ^ 2/2,

where m is the mass of the bullet, m = 10 g = 0.01 kg;

V is the speed of the bullet; V = 50 m / s.

Neglecting the energy losses for heating the bullet and sand, we consider that the kinetic energy of the bullet is converted into the potential energy of the box with sand and the bullet. Then:

E = (M + m) gH,

where M is the mass of the box with sand; g is the acceleration of gravity.

We get:

mV ^ 2/2 = (M + m) gH, whence the required height H:

H = mV ^ 2 / [2g (M + m)] = 0.01 × 50 ^ 2 / [2 × 9.8 × (50 + 0.01)] = 0.0255 m = 25.5 mm.