Question

Two projectiles thrown at 30° and 45° with the horizontal, respectively, reach the maximum height in same time. The ratio of their initial velocities is :

• A. $1:\sqrt 2$
• B. $2:1$
• C. $\sqrt 2:1$
• D. $1:2$

Answer 1

Answer: (C)

$\sqrt 2:1$

Answer 2

We know that,
$t_a=\frac {u\ sin⁡\ θ}{g}$

$⇒\frac {u_1sin⁡(30^∘)}{g}=\frac {u_2sin⁡(45^∘)}{g}$
The ratio of their initial velocities is:
$⇒\frac {u_1}{u_2}=\frac {\frac {1}{\sqrt 2}}{\frac 12}$

$⇒\frac {u_1}{u_2}=\frac {\sqrt 2}{1}$

So, the correct option is (C): $\sqrt 2:1$