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Question

A body is projected up a smooth inclined plane (length = 202m ) with velocity u from the point M as shown in the figure. The angle of inclination is 45 and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v


A

40 ms1

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B

40 2 ms1

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C

20 ms1

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D

20 2 ms1

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Solution

The correct option is D

20 2 ms1


At point N angle of projection of the body will be 45. Let velocity of projection at this point is v. If the body just manages to cross the well then

Range = Diameter of well

v2 sin 2 θg=40 [As θ=45]v2=400 v=20 m/s

But we have to calculate the velocity (u) of the body at point M.

For motion along the inclined plane (from M to N)

Final velocity (v) = 20 m/s, acceleration (a) = g sin α=g sin 45, distance of inclined plane (s) = 202m

(20)2=u22 g2.202 [Using v2=u2+2as]u2=202+400 u=202m/s.


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