Question

If $t_1$ and $t_2$ are the times of flight of two particles having the same initial velocity $u$ and range $R$ on the horizontal, then $t_1^2+t_2^2$ is equal to: (Assuming their angle of projection is not equal)

• A. $\frac{u^2}{g}$
• B. $\frac{4u^2}{g}$
• C. $\frac{u^2}{2g}$
• D. $1$

Answer 1

Answer: (B)

$\frac{4u^2}{g}$

Since both have same range their sum of angles should be $90$

$t_1=\frac{2u\sin \theta }{g}$

$t_2=\frac{2u\cos \theta }{g}$

$t_1^2+t_2^2=\frac{4u^2{\sin }^2\theta }{g^2}$ $+\frac{4u^2{\cos }^2\theta }{g^2}$

$t_1^2+t_2^2=\frac{4u^2}{g^2}$