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) $(g = 10 m / s^{2})$

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$u = 4 \sqrt{5} m / s, θ = 45^{0}$

$u = 4 \sqrt{5} m / s, θ = \tan^{- 1} (3)$

$u = 2 \sqrt{5} m / s, θ = 45^{0}$

$u = 8 \sqrt{5} m / s, θ = \tan^{- 1} (3)$

answer is A, B.

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Detailed Solution

$y = x \tan θ - \frac{1}{2} \frac{g x^{2}}{u^{2} \cos^{2} θ}$
A) $2 = 4 \times 1 - \frac{1}{2} \times \frac{10^{2} \times 4^{2}}{16 \times 5 \times \frac{1}{2}}$
B) $2 = 4 \times 3 - \frac{1}{2} \times \frac{10^{2} \times 4^{2}}{16 \times 5 \times \frac{1}{2}} = 0$
C) $2 = 4 \times 2 - \frac{1}{2} \times \frac{10^{2} \times 4^{2}}{4 \times 5 \times 1} = 0$