Question

A shot travelling at the rate of 200m/s is just able to pierce a plank 5cm thick. The velocity required to pierce a small plank 20cm thick

Answer 1

so initial velocity of the shot, u=200m/s
distance travelled before coming to rest,S= 5cm= 0.05m
final velocity, v=0
let the retardation be 'a'
we know,
v^2=u^2-2aS
or, 0= 40000-2a*0.05
or,a=40000/(2*0.05)
or, a= 4*10^5 m/sec^2

let the initial velocity required to pierce 20cm i.e 0.2m before coming to rest be 'u'm/sec
final velocity, v=0 m/sec
applying, v^2=u^2-2aS
0=u^2-2*4*10^5*0.2
or, u^2= 16*10^4
or, u= sqrt(16*10^4)
or, u=400 m/sec
the required velocity= 400m/sec