Question

Two bodies are thrown at angle $\theta$ and $(90-\theta )$ from the same point with same velocity $25m{s}^{-1}$. If the difference between their maximum height is $15m$, find the respective maximum heights.
$(g=10m{s}^{-2})$

• A. $H_1=\frac{85}{8}m$ and $H_2=\frac{175}{8}m$
• B. $H_1=\frac{185}{8}m$ and $H_2=\frac{65}{8}m$
• C. $H_1=\frac{65}{4}m$ and $H_2=\frac{135}{8}m$
• D. $H_1=\frac{125}{4}m$ and $H_2=\frac{65}{8}m$

Answer 1

The correct option is B $H_1=\frac{185}{8}m$ and $H_2=\frac{65}{8}m$

Let $H_1$ and $H_2$ be the maximum heights of the bodies thrown at angles $\theta$ and $90-\theta$ respectively.
$H_1=\frac{u^2{\sin }^2\theta }{2g}\text{and}{H}_2=\frac{u^2{\sin }^2(90-\theta )}{2g}=\frac{u^2{\cos }^2\theta }{2g}$
$\Rightarrow H_1+H_2=\frac{u^2}{2g}$
$H_1+H_2=\frac{{25}^2}{20}=\frac{125}{4}m.......\text{(i)}$
According to queston
$H_1-H_2=15m........\text{(ii)}$
By using equ. $\text{(i)}$ and $\text{(ii)}$, we get
$H_1=\frac{185}{8}m$ and $H_2=\frac{65}{8}m$