Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R

Question

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ______ m. (Take g = 10 ${m/s}^{2}$ ) [2026]

Smart Achievers · Accepted Answer

(1)

$For range to be same, angle of projection must be complementary angles.$

$T_{1} = \frac{2 u \sin θ}{g} = 10 s,$ $T_{2} = \frac{2 u \cos θ}{g} = 5 s$

$Range = \frac{2 (u \sin θ) (u \cos θ)}{g} = 250 m$

Solution

Q.
Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ______ m. (Take g = 10 ${m/s}^{2}$ ) [2026]

1 250

2 25

3 500

4 125

Ans.
(1)

$For range to be same, angle of projection must be complementary angles.$

$T_{1} = \frac{2 u \sin θ}{g} = 10 s,$ $T_{2} = \frac{2 u \cos θ}{g} = 5 s$

$Range = \frac{2 (u \sin θ) (u \cos θ)}{g} = 250 m$

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