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Question

# The equation of motion of a projectile is : y=12x−3/4x2 Given that g=10ms−2, what is the range of the projectile ? (in metres)

A
16
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B
12
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C
20
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D
24
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Solution

## The correct option is A 16Given, y=12x−34x2The general equation of a projectile motion is given by, y=xtanθ−g2u2cos2θx2Comparing both equation, we get tanθ=12 and g2u2cos2θ=34Now, u2cos2θ=(4/3)(g/2)=(4/3)(10/2)=40/6=20/3⟹ ucosθ=√20/3Also, from tanθ=12 We get sinθcosθ=12⟹ usinθ=12ucosθ=12×√20/3Range of a projectile motion is given by, R=u2sin2θg ∴ R=u2(2sinθcosθ)g=2(12√20/3)(√20/3)10=20×243×10=16 m

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