Question

Two bodies are projected from the same point in directions inclined at ${60}^0$ and ${30}^0$ to the horizontal.If they attain the same maximum height, the ratio of their velocity of projection is:

• A. $1:\sqrt{3}$
• B. $\sqrt{3}:1$
• C. 1:2
• D. 1:1

Answer 1

The correct option is A $1:\sqrt{3}$

We have the equation for height, $H=\frac{u^{2}si{n}^2\theta }{2g}$

If the two bodies attain the same maximum height, the ratio of their velocity of projection,

$\frac{u_1^{2}si{n}^2{60}^2}{2g}=\frac{u_2^{2}si{n}^2{30}^2}{2g}$

$\frac{u_1^2}{u_2^2}=\frac{(\frac{1}{2}{)}^2}{(\frac{\sqrt{3}}{2}{)}^2}$

$⟹u_1:u_2=1:\sqrt{3}$