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

Answer

D

Explanation

Angle of projection form B is `45^(@)`. As the body is able to cross the well of diameter 40m, hence
or `R=(v^(2))/g or v=sqrt(gR)`
`v=sqrt(10xx40)=20ms^(-1)`
On the inclined plane, the retardation is:
`gsin alpha=g sin 45^(@)=10/(sqrt(2))ms^(-2)`
Using `v^(2)-u^(2)=2ax`
`(20)^(2)-u^(2)=2xx(-10/(sqrt(2)))xx20sqrt(2)`
`u=20sqrt(2)ms^(-1), i.e, V=20sqrt(2)ms^(-1)`