A projectile is projected into air with certain velocity making an angle α with horizontal. It passes through the points P(10m, 20m) and Q(20m, 10m) in its path along the plane before striking the ground. The horizontal range of the projectile is

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$\frac{52}{3} m$

$\frac{70}{3} m$

$\frac{56}{3} m$

$\frac{44}{3} m$

answer is D.

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Detailed Solution

We know that $y = xtan θ \{1 - \frac{x}{R}\}$
At, P $20 = 10 \tan α \{1 - \frac{10}{R}\}$
At Q, $10 = 20 \tan α \{1 - \frac{20}{R}\}$
After simplification , $R = \frac{70}{3} m$

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