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Question

For a given velocity, a projectile has the same range R for two angles of projection if t1 and t2 are the time of flight in the two cases, then:

A
t1t2R
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B
t1t2R2
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C
t1t21R2
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D
t1t21R
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Solution

The correct option is B t1t2R
The range of a projectile motion is given as R=2u2sinθcosθg
It two projectiles with same velocity have same range,
R=2u2sinθ1cosθ1g=2u2sinθ2cosθ2g
θ2=90θ1
Thus, the times of the flights are:
t1=2usinθ1g
t2=2usinθ2g=2ucosθ1g
Thus, t1t2sinθ1cosθ1R

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