Question

A 15-g bullet is fired horizontally into a 3.000-kg block of wood suspended by a long cord. The bullet sticks in the block. Compute the speed of the bullet if the impact causes the block to swing 10 cm above its initial level.

Initial Velocity of bullet=19.1m/s

Answer 1

Use the distance of upward swing to compute the velocity right after impact.

M (9.8 m/s^2)(0.1 m) = (1/2) M V^2
V = sqrt(2 g H) = 1.4 m/s

Now use conservation of momentum, applied to the bullet impact, for the bullet velocity, Vb.

m Vb = (M + m)*1.4 m/s
Vb = 1.4*(3.015/.015) = 281 m/s

That des not agree with what you wrote.