A bullet enters a wooden block with velocity 120 m/s. The bullet travels 1.5 s in the block before its velocity reduces to zero due to resistance force which is proportional to the square root of the velocity. The distance travelled by the bullet in the wooden block is

Options

A. 10 m
B. 60 m
C. 25 m
D. 90 m

Explanation

Given velocity of bullet, u=120 m/s and t=1.5s
If deceleration of bullet inside the block is a.
Then from the first equation of motion, `v=u-at`
`0=120-axx1.5`
`impliesa=(120)/(1.5)=80m//s^(2)`
If bullet travels a distance of s meter before it comes to rest, from thrid equation of the motion,
`v^(2)=u^(2)-2as`
`0=120^(2)-2xx80xxs`
`impliess=(120xx120)/(2xx80)=90m`
Hence, option D is correct.