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Question

An inclined plane makes as angle θ0=30 with the horizontal. A particle is projected from this plane with a speed of 5 m/s at an angle of elevation β=30 with the horizontal as shown in the figure.


Find the range of the particle on the plane when it strikes the plane. (Assume the incline is long enough and g=10 m/s2)

A
3.5 m
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B
4 m
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C
4.2 m
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D
5 m
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Solution

The correct option is D 5 m
Angle of inclination with the inclined surface, α=θ0+β=60
Range on incline, R=u2gcos2θ0[sin(2αθ0)+sinθ0]
=5210cos230[sin(2×6030)+sin30]
=2510×(32)2[sin90+12]
=25×410×3×32
= 5 m

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