A heavy block `B` is sliding with constant velocity `u=5m//s` on a horizontal table. The width of the block is `L=4m`.
There is an insect `A` at distance `d=3m` from the block as shown in the figure. The insect wants to cross to the oposite side of the table. It begins to crawl at a constant velocity `v` at the instant shown in the figure. Find the least value of `v` (in m/s) for which the insect can cross to the other side without getting hit by the block.

Answer

4

Explanation

Time to cross `t=L/(vcostheta)`
`:.ut+d+Ltantheta=(uL)/(vcostheta)`
`:.v=(uL)/(dcostheta+Lsintheta)`
`:.v_("min")=(uL)/(sqrt(d^(2)+L^(2)))=4m//s`