A block of mass `1 kg` is horizontal thrown with a velocity of `10 ms^(-1)` on a stationary long of mass `2 kg` whose surface has a `mu = 0.5`. Plane rest on friction surface find the time when `m_(1)` comes to rest w.r.t. plane

Explanation

`a_(1) =- (mu m_(1) g)/(m_(1)) = - mu g` and `a_(2) = (mu m_(1) g)/(m_(2))`
`:. a_(rel) = a_(1) - a_(2) = - mu g - mu (m_(1) g)/(m_(2)) rArr a_(rel) = - 5 - 0.5 (1)/(2) xx 10`
`a_(rel) = - 5 - (5)/(2) = - 7.5 ms^(-2)`
`v_(rel) = 0, mu_(rel) = v_(0)`
`:. v_(rel) = u_(rel) + u_(rel) t or 0 = v_(0) - 7.5 t`
`:. t = (v_(0))/(7.5) = (10)/(7.5) = (4)/(3) s`