KinematicsMedium
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 $g = 10\text{ }m/s^{2}$ )
Options
A.250
B.25
C.500
D.125
Solution
Sol. [Key Concept: Equal ranges occur for complementary angles, so $T_{1}T_{2} = \frac{2usin\theta}{g} \cdot \frac{2ucos\theta}{g}$ and $R = \frac{1}{2}\ {gT}_{1}T_{2} = 250$ m.]
For range to be same, angle of projection must be complementary angles.
$$T_{1} = \frac{2usin\theta}{g} = 10,{\text{ }T}_{2} = \frac{2ucos\theta}{g} = 5 $$Range $= \frac{2(usin\theta)(ucos\theta)}{g}$
$$= \frac{2(50)(25)}{10}\text{ }m = 250\text{ }m $$
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