Question

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

Answer 1

$\text{Step 1: Equation of Trajectory [Refer Fig. 1] [Refer Fig. 2]}$

Let $h$ be the height of the pole

Using the equation of trajectory

$y=x\tan \alpha (1-\frac{x}{R})$

$R=$ Range of the projectile

$=a+b$ [From diagram]

$\text{Step 2: Calculate height of the pole}$

$x=a$; $\alpha ={45}^{\circ }$; $y=h$

$\therefore h=a\tan 45(1-\frac{a}{a+b})$

$=\frac{ab}{a+b}$