Question

A bullet with some mass, m, and initial speed, vi, collides with a wooden block of mass M
that is hanging at the end of a light rope. The bullet imbeds itself in the block and the block
and bullet swings upwards reaching a maximum height of h above the initial point of the
collision.
a. A scientist can measure the masses and the height, show that the initial speed
can then be calculated from the following equation:
vi= (m+M)/m×root 2gh
Show all of your work starting from the principles of conservation of momentum and energy. Do
not use kinematics or any pre-existing ballistic pendulum equations to solve.
b. The bullet has a mass of 25 g and the block is 5.000 kg. If h = 6.40 cm, find the
initial speed of the bullet.

Answer 1

- initial velocity V; = ? final velocity Vp =V - UEV V = V₂ =V E I M .mt M mass of bullet 'm' .. mass of block"M' . momentum before collision = momentum after collisia mu,+ m₂ = (m, tm, v mvi + MCO) - (m_M) V ✓ = (m+M) V mi

Now KE just after collision = PE after the bloce reaching height I mvz = Mgh mv² =augh | v = vàng h) r = V2ghi Vi= mtm xv. fri = mtm dagh - m b) m = 25g = 25x 103kg M = 25 kg h 6.4cm = 6:48 10 M substituting. V - XV 2x9.8) 6.4x102 25*10° +5 25x103 5.025-xV1-25568 = 0.0Qs = 225.234 m/s .