Question

From a point on the ground at a distance $a$ from the foot of pole,a ball is thrown at an angle of ${45}^o$, which just touches the top of the pole and stickers the ground at a distance of $b$, on the other side of it. Find the height of the pole.

• A. $\frac{ab}{a+b}$
• B. $\frac{ab}{a-b}$
• C. $\frac{2ab}{a+b}$
• D. $\frac{a+b}{a+2b}$

Answer 1

The correct option is A $\frac{ab}{a+b}$

Two dimensional projectile

$x=u\cos \varphi \times t=\frac{ut}{\sqrt{2}}$ as $\varphi =\frac{\pi }{4}$

and $y=u\sin \varphi t-\frac{1}{2}g{t}^2=\frac{4}{\sqrt{2}-\frac{1}{2}g{t}^2}$

$y=\frac{x-g{x}^2}{u^2}$ as $\tan \varphi =1$ and $\cos \varphi =\frac{1}{\sqrt{2}}$

When $x=a$, $y=h$

$h=\frac{a-g{a}^2}{u^2}--------\left(i\right)$

$u^2=g(a+b)--------\left(ii\right)$

Substituting this $\left(ii\right)$ in $\left(i\right)$ we get,

$h=\frac{-a^2}{a+b}=\frac{a\times b}{a+b}$