A body is projected up a smooth inclined plane with velocity V from the point A as shown in the figure. The angle of inclination is `45^(@)` and the top is connected to a well of diameter 40m. If the body just manages to across the well, what is the value of V? Length of inclined plane is `20sqrt(2)m`.

Options

A. `40 m s^-1`
B. `40 sqrt(2) m s^-1`
C. `20 ms^-1`
D. `20 sqrt(2) ms^-1`

Answer

D

Explanation

(d) Angle of projection from `B is 45^@`. As the body is able to cross the well of diameter `40 m`, hence
`R = (v^2)/(g) or v =( sqrt(g R)) = (sqrt(10 xx 40)) = 20 ms^-1`
On the inclined plane, the retardation is
`g sin prop = g sin 45^@ = 10// (sqrt(2)) ms^-2`
Using `v^2 - u^2 = 2ax`
`(20)^2 - u^2 = 2 xx (-(10)/(sqrt(2))) xx 20 (sqrt(2))`
`u = 20 (sqrt(2)) ms^-1`.