A projectile has same range R for two angles of projection. If T₁ and T₂ be the times

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3-2.Motion in Plane

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A projectile has the same range $R$ for two angles of projection. If $T_1$ and $T_2$ be the times of flight in the two cases, then $R$ is

A

$T_1T_2g$

B

$\frac{T_1T_2g}{2}$

C

$(T_1^2 + T_2^2)g$

D

$\frac{(T_1^2 + T_2^2)}{2}g$

Solution

$\mathrm{T}_{1}=\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}}, \mathrm{T}_{2}=\frac{2 \mathrm{u} \cos \theta}{\mathrm{g}}$

and $\mathrm{R}=\frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}} \Rightarrow \mathrm{R}=\frac{\mathrm{T}_{1} \mathrm{T}_{2} \mathrm{g}}{2}$

Standard 11

Physics

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