A bullet of mass 25 g is fired horizontally into a 5.0 kg ballistic pendulum and becomes embedded within it, as shown in the figure. If the centre of the pendulum rises by a distance of 10 cm , determine the speed of the bullet.

Step-by-step solution

Let m be the mass of the bullet, M be the mass of the pendulum, v be the initial speed of the bullet, and V be the speed of the combined mass just after the collision. By conservation of linear momentum: m v = (m + M) V V = m v m + M By conservation of mechanical energy after the collision, as the pendulum rises to a height h : 1 2 (m + M) V^2 = (m + M) g h V = 2 g h Equating the two expressions for V : m v m + M = 2 g h v = ( m + M m ) 2 g h Given m = 25 g = 0.025 kg , M = 5.0 kg , h = 10 cm = 0.1 m , and taking g