Question

A ball is thrown at different angles with the same speed u and from the same point. It has the same range in both cases. It $y_1$ and $y_2$ be the heights attained in the two cases, then $y_1+y_2$ equals to

• A. $\frac{u^2}{g}$
• B. $\frac{2u^2}{g}$
• C. $\frac{u^2}{2g}$
• D. $\frac{u^2}{4g}$

Answer 1

The correct option is C $\frac{u^2}{2g}$

As the ball thrown has same range, the angles of projections are $\theta$ and $90-\theta$. So,

$y_1=\frac{u^{2}si{n}^2\theta }{2g}$ and $y_2=\frac{u^{2}si{n}^2(90-\theta )}{2g}$

Then,

$y_1+y_2=\frac{u^2}{2g}si{n}^2\theta +\frac{u^2}{2g}co{s}^2\theta$

$y_1+y_2=\frac{u^2}{2g}(si{n}^2\theta +co{s}^2\theta )$

$y_1+y_2=\frac{u^2}{2g}$