A wooden block of 5.0 kg mass lies on a horizontal wooden table. A bullet of 9.0 g mass hits the block after which it moves a distance 25 cm across the table before stopping. Find the bullet's speed.

Answer

670 m/s

Explanation

Take the coordinate axis to coincide with lhe direction of the bullet.s flight. Let the mass of the bullet be m and the mass of the block be M. By the law of conservation of momentum mv = (M + m) u, where v and u are the projections of the velocity of the bullet and of the block after it is hit by the bullet. A force of friction acts on the sliding block in the opposite direction to the velocity vector: T = = - µg (M + m). The acceleration of the block is `a= T//(M + m) = = -µg`. The block comes lo rest after travelling a distance l, therefore `O - u^(2) = 2al` , or `u = -sqrt(2µgl)`. Hence
`v=(M+m)/msqrt(2mugl)`
Substituting numerical values and noting that `m ltlt `M, we obtain the value of the velocity cited in the answer.