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Question

A projectile is projected from the level ground in vertical x-y plane (vertical is y axis). The point of projection is considered as the origin. For which of the following initial velocities of projection u and angle of projection θ with the horizontal will the projectile pass through the point (4, 2) (all in m) (Neglect air friction)

A
u=45 ms,θ=45
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B
u=45 ms,θ=tan1(3)
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C
u=25 ms,θ=45
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D
u=85 ms,θ=tan1(3)
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Solution

The correct options are
A u=45 ms,θ=45
B u=45 ms,θ=tan1(3)
x=uxt=(u cos θ)t
t=xu cos θ
Also, y=uyt12gt2
y=(u sin θ)xu cos θ12g(xu cos θ)2
y=x tan θgx22u2 cos2 θ
(A) 2=4×11210×4216×5×12
(B) 2=4×31210×4216×5×110
(C) 2=4×11210×424×5×12
(D) 2=4×31210×4264×5×110

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