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 kinematic equation, aligned & v^2=u^2+2 a s & ( 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, v^2=u^2+2 as 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 =10 ~cm aligned