Find unit vector in direction of friction force acting on block placed on plank 'p' (Given : `bar(V)_(P)=7i - 2j,bar(V)_(B)=3hat(i)+hat(j)`)

Options

A. `(4)/(5)hat(i)-(3)/(5)hat(j)`
B. `(4)/(5)hat(i)-(3)/(5)hat(k)`
C. `(4)/(5)hat(j)-(3)/(5)hat(i)`
D. `(4)/(5)hat(i)+(3)/(5)hat(j)`

Answer

D

Explanation

`v=(ds)/(dt)=12-4t" "therefore" "u = 12 m//s" and "a=-4m//s^(2),t_(0)=|(u)/(a)|=3s`
Here, `t_(0)` is the time when velocity becomes zero. Since, the given time t = 5s is greater then `t_(0)`. The distance
`d=|(u^(2))/(2a)|+|(1)/(2)a(t-t_(0))^(2)|=(144)/(2xx4)+(1)/(2)xx4xx4=18+8=26m`