Question

A ball is thrown at different angles with the same speed u and from the same points and it has same range in both the cases. If $y_1$ and $y_2$ be the heights attained in the two cases, then $y_1+y_2=$

• 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 $\frac{u^2}{2g}$

Same ranges can be obtained for complementary angles i.e. $\theta$ and ${90}^{\circ }-\theta$
$y_1=\frac{u^{2}si{n}^2\theta }{2g}and{y}_2=\frac{u^{2}co{s}^2\theta }{2g}{y}_1+y_2=\frac{u^{2}si{n}^2\theta }{2g}+\frac{u^{2}co{s}^2\theta }{2g}=\frac{u^2}{2g}$