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 y₁ and y₂ 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

Answer: (C)

$\frac{u^{2}}{2g}$

Answer 2

Same ranges can be obtained for complementary angles i.e. $\theta$and 90^o – $\theta$

$y_{1} = \frac{u^{2}\sin^{2}\theta}{2g}$and $y_{2} = \frac{u^{2}\cos^{2}\theta}{2g}$

∴ $y_{1} + y_{2} = \frac{u^{2}\sin^{2}\theta}{2g} + \frac{u^{2}\cos^{2}\theta}{2g} = \frac{u^{2}}{2g}$