Question

A ball is thrown from the ground level so as to just clear a wall at a distance of $a$ meters and it falls at a distance of $b$ meters from the foot of the wall. If the angle of projection is ${45}^{\circ }$, find the height of the wall.

• A. $h=\frac{a}{a+b}$
• B. $h=\frac{b}{a+b}$
• C. $h=\frac{ab}{a+b}$
• D. $h=ab$

Answer 1

The correct option is C $h=\frac{ab}{a+b}$

Let the given condition be as shown in the below figure

Given, $\theta ={45}^{\circ }$
Let $h$ be the height of the wall
From the figure, $R=a+b$
By equation of trajectory of a projectile, we know
$y=x\tan \theta (1-\frac{x}{R})\Rightarrow h=a\left(1\right)(1-\frac{a}{a+b})$
$\Rightarrow h=\frac{ab}{a+b}$