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Question:

A particle is projected with an angle of projection to the horizontal line passing through the points (P, Q) and (Q, P) referred to horizontal and vertical axes (can be treated as x-axis and y-axis respectively). The angle of projection can be given by?

tan⁻¹[P²+PQ+Q²/PQ]

tan⁻¹[P²+Q²-PQ/PQ]

sin⁻¹[P²+Q²+PQ/2PQ]

tan⁻¹[P²+Q²/2PQ]

Solution:

Correct option is A. tan⁻¹[P²+PQ+Q²/PQ]
Given that, A particle is projected with an angle of projection to the horizontal line passing through the points (P,Q) and (Q,P).
The general equation of path for projectile motion is
y = x tanθ + gx²/2u²(cos θ)²
Now, since the above equation passes through (P,Q) and (Q,P) so, we will get two equations as
P = Qtanθ - gQ²/2u²(cos θ)² (I)
Q = Ptanθ - gP²/2u²(cos θ)² (II)
From equation (I) and (II) after solving
θ = tan⁻¹[P²+PQ+Q²/PQ]
So, The angle of projection is θ = tan⁻¹[P²+PQ+Q²/PQ]
Hence, A is correct option.