A bullet fired into a large block of wood of uniform resistance, hits the block with a velocity of 48 m/s.It penetrates a distance of 60 cm and the velocity is then reduced to 24m/s. It then penetrates a further distance of (in cm)?

Let the initial velocity be u and constant retardation be a.

Then
v² = u² - 2aS

(24)² = (48)² - 2a(60)
or, 120a = 2304 - 576 = 1728

or, a = 14.4 m/s²

Let the bullet covers a total distance of x .
Then using the same acceleration we get:

0² = u² - 2ax.
 0 = 2304 - (2x14.4)(x)

x = 2304/(2x14.4) = 80cm.

So, the bullet covers a total a 80 cms into the target or the bullet goes furthur by 20 cms.

 

Hope this helps,

Team Topper