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Question

The trajectory of a projectile near the surface of the earth is given as y=2x9x2. 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 options are
B Angle of projection is cos1(15)
D Speed of projection is 53 m/s
Equation of Trajectory for projectile is,
y=2x9x2 ...(i)
The standard equation of trajectory for a projectile,
y=xtanθgx22u2cos2θ ...(ii)
On comparing Eq.(i) and (ii),
tanθ=2 ...(iii)
& g2u2cos2θ=9 ...(iv)


From Eq.(iii)
tanθ=2=21
cosθ=15 [From diagram]
θ=cos1(15)
Similarly,
sinθ=25 [From diagram]
θ=sin1(25)
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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