A bullet is fired on a target with velocity ' V '. Its velocity decreases from ' V ' to ' V / 2 ' when it penetrates 30 ~cm in a target. Through what thickness it will penetrate further in the target before coming to rest?

Step-by-step solution

When the velocity of the bullet changes from V to V 2 the distance travelled by the bullet is 30 ~cm . Using 3^ rd equation of motion, aligned & v ^2= u ^2+2 a & ( V 2 )^2= V ^2+2 a (30) & V ^2 4 = V ^2+60 a & -3 ~V ^2 4 =60 a & a = - V ^2 80 aligned Further, when a bullet penetrates it comes to rest. So, the final velocity of the bullet becomes zero. Using the relation, aligned & v ^2= u ^2+2 as & 0= ( V 2 )^2+2 (- V ^2 80 ) s & V ^2 4 = ( V ^2 40 ) s & s = 40 4 & ~s =10 ~cm aligned