A block of mass `1kg` is pushed on a movable wedge of mass `2kg` and height `h=30 cm` with a velocity `u=6m//sec`. Before striking the wedge it travels `2m` on a rough horizontal portion. Velocity is just sufficient for the block to reach the top of the wedge. Assuming all surface are smooth except the given horizontal part and collision of block and wedge is jerkless, the friction coefficient of the rough horizontal part is `:`
An observer having a gun observes a remotely controlled balloon. When he first noticed the balloon, it was at an altitude of `800m` and moving vertically upward at a constant velocity of `5m//s`. The horizontal displacement of balloon from the observer is `1600m`. Shells fired from the gun have an initial velocity of `400 m//s` at a fixed angle `theta ( sin theta =3//5 `and `cos theta =4//5 )`. The observer having gun waits `(` for some time after observing the balloon) and fires so as to destroy the balloon. Assume `g=10m//s^(2)`. Neglect air resistance.

Options

A. `0.125`
B. `0.377`
C. `0.675`
D. `0.45`

Answer

C

Explanation

velocity of the block after passing through the rough surface is `v=sqrt(36+2mug(2))=sqrt(36-40mu)`
Apply work energy theorem
`mu mg (2)+mgh=KE_(i)-KE_(f) ...(1)`
at the highest point
`V_(block)=V_(wed g e)`
`2-mu+3=(1)/(2)1(6)^(2)-(1)/(2)3v^(2)`
`mu=(54)/(80)=0.675`