A penguin of mass `m` stands at the right edge of a sled of mass `3m` and length `l`. The sled lies on frictionless ice. The penguin starts moving towards left,reaches the left end and jumps with a velocity `u` and at an angle `theta` relative to ground. `(` Neglect the height of the sled `)`

Options

A. Till the penguin reaches the left end, the sled is displaced by `(l)/(4)`
B. Till the penguin reaches the left end, the sled is displaced by `(l)/(3)`
C. After jumping, it will fall on the ground at a distance `(4)/(3) (u^(2)sin2 theta)/(g)` from the left end of the sled.
D. After jumping, it will fall on the ground at a distance `(3)/(4) (u^(2) sin 2 theta)/(g)` from the left end of the sled.

Answer

A, C

Explanation

`(A) S_(m)=(m_(1)S_(1)+m_(2)S_(2))/(m_(1)+m_(2))`
`0=((3m)(-x)+(m)(l-n))/(3m+m)`
`x=(l)/(4)`
`(C )` ,
`T=(2u sin theta )/(g)`
Displacement of sled in this time
`=((u cos theta )/(3))((2u sin theta )/(g))=(1)/(3)((u^(2) sin 2 theta )/(g))`
Total distance `=(4)/(3)((u^(2) sin 2 theta)/(g))`