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

Question

Two projectile thrown at 30 &#176; and 45 &#176; with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

Aicharya · Accepted Answer

Time taken to reach maximum height is given by
$t = \frac{u \sin θ}{g}$ , where, $u$ is initial velocity.
Here, $t_{1} = t_{2}$
$∴ \frac{u_{1} \sin θ_{1}}{g} = \frac{u_{2} \sin θ_{2}}{g}$
$\Rightarrow u_{1} \sin 30 = u_{2} \sin 45$
$\Rightarrow \frac{u_{1}}{u_{2}} = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} = \frac{\sqrt{2}}{1} = \sqrt{2} : 1$

Two projectile thrown at 30 ° and 45 ° with the horizontal respectively, reach the maximum height…

Solution

Two projectile thrown at 30 &#176; and 45 &#176; with the horizontal respectively, reach the maximum height…

Solution

Two projectile thrown at 30 ° and 45 ° with the horizontal respectively, reach the maximum height…