Question

A particle is thrown with velocity u at an angle $\alpha$ from the horizontal. Another particle is thrown with the same velocity at an angle $\alpha$ from the vertical. The ratio of times of flight of two particles will be

• A. $tan2\alpha :1$
• B. $cot2\alpha :1$
• C. $tan\alpha :1$
• D. $cot\alpha :1$

Answer 1

The correct option is C

$tan\alpha :1$

For first particles angle of projection from the horizontal is a. So $T_1=\frac{2usin\alpha }{g}$

For second particle angle of projection from the vertical is $\alpha$. it mean from the horizontal is $90-\alpha$

$\therefore T_2=\frac{2usin(90-\alpha )}{g}=\frac{2ucos\alpha }{g}.$ So ratio of time of flight $\frac{T_1}{T_2}=tan\alpha$.