Question

A bullet of mass m=26g is fired into a wooden block of mass M=4.7kg. The block is attached to a string of length 1.5m. The bullet is embedded in the block, causing the block to then swing. If the block reaches a maximum height of h=0.31m, what was the initial speed of the bullet?

Answer 1

u = 449 m/s

Step-by-step explanation:

Given,

Mass of the bullet, m = 26 g

Mass of the wooden block,M = 4.7 Kg

height of the block,h = 0.31 m

initial speed of the block, u = ?

Using conservation of energy

`(M+ m)gh = (1)/(2)(M+m)v^2`

`gh = (1)/(2)v^2`

`v=√(2gh)`

`v=√(2* 9.81* 0.31)`

v = 2.47 m/s

Now, using conservation of momentum to calculate the speed of the bullet.

m u + M u' = (M+m)v

m u = (M+m)v

0.026 x u = (4.7+0.026) x 2.47

u = 449 m/s

Hence, the speed of the bullet is equal to 449 m/s.