A bullet from a gun is fired on a rectangular wooden block with velocity u. When the bullet travels 24 cm through the block along its length horizontally, the velocity of the bullet becomes u/3. It then further penetrates into the block in the same direction before coming to rest exactly at the oth…

Question

A bullet from a gun is fired on a rectangular wooden block with velocity u. When the bullet travels 24 cm through the block along its length horizontally, the velocity of the bullet becomes u/3. It then further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is

Accepted Answer

(4) 27 cm. Given: entry speed u, speed u/3 after 24 cm, uniform retardation a, final speed zero. Idea: apply v²=u²-2as over the two stretches and divide, so the unknown retardation cancels. First stretch: (u/3)²=u²-2a(24), so 2a(24)=u²-(u²)/9=(8u²)/9. Remaining stretch s: 0=(u/3)²-2as, so 2as=(u²)/9. Dividing: s/(24)=(u²)/9×9/(8u²)=1/8, so s=3 cm. Total penetration =24+3=27 cm.

Step-by-step solution

Why the other options are wrong