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Question

# The trajectory of a projectile near the surface of the earth is given as y=2x−9x2. Then choose the correct option(s): [Take g=10 m/s2]

A
Angle of projection is sin1(15)
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B
Angle of projection is cos1(15)
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C
Speed of projection is 35 m/s
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D
Speed of projection is 53 m/s
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Solution

## The correct option is D Speed of projection is 53 m/sEquation of Trajectory for projectile is, y=2x−9x2 ...(i) The standard equation of trajectory for a projectile, y=xtanθ−gx22u2cos2θ ...(ii) On comparing Eq.(i) and (ii), tanθ=2 ...(iii) & g2u2cos2θ=9 ...(iv) From Eq.(iii) tanθ=2=21 ⇒cosθ=1√5 [From diagram] ⇒θ=cos−1(1√5) Similarly, sinθ=2√5 [From diagram] ⇒θ=sin−1(2√5) From Eq.(iv), 102×u2×(15)=9 ⇒u=√5×59 ∴u=53 m/s Here θ is the angle of projection and u is the initial speed of projectile.

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