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Question

# A ball is projected horizontally with a speed v from the top of a plane inclined at an angle 45∘ with the horizontal. How far from the point of projection will the ball strike the plane?

A
v2g
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B
2v2g
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C
2v2g
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D
2[2v2g]
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Solution

## The correct option is D √2[2v2g]Let the distance along inclined plane be l at which the ball will strike. Let the horizontal distance covered by the ball before striking be x. ⇒x=vt(1) Vertical distance covered by the ball is given by y=12gt2(2) Using value of t from (1) in (2), we get y=gx22v2 From the figure, tan45∘=yx or y=xx=gx22v2⇒x=2v2g⇒y=2v2g From the figure, we get, l2=x2+y2l=√2[2v2g]

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