Question

If the ratio of the maximum heights attained by two balls on being thrown vertically upwards is 3:5, what is the ratio of the velocities with which they were thrown upwards? URGENT ⚠️

Answer 1

Given

The ratio of the maximum heights attained by two balls on being thrown vertically upwards is 3:5.

To Find

The ratio of their maximum height.

Formulas involved

$\boxed{h\:=\: \dfrac{u^2}{2g}}$

$\implies \: u^2\:=\:2gh$

Calculations

Let the heights reached by balls be $h_1\:and\:h_2$ respectively.

Therefore, $\dfrac{h_1}{h_2}\:=\: \dfrac{3}{5}$

Ratios of their initial velocity = $\dfrac{u^2_1}{u^2_2}$

$\implies \: \dfrac{u^2_1}{u^2_2}\:=\: \dfrac{2gh_1}{2gh_2}$

$\implies \: \dfrac{u^2_1}{u^2_2}\:=\: \dfrac{h_1}{h_2}$

$\implies \: \dfrac{u^2_1}{u^2_2}\:=\: \dfrac{3}{5}$

$\implies \: \dfrac{u_1}{u_2}\:=\: \sqrt{\dfrac{3}{5}}$

$\boxed{u_1:u_2\:=\: \sqrt{3} : \sqrt{5}}$

Answer 2

The answer is √3:√5 beacause u = √2gh