Question

A particle is projected so as to graze the top of two walls each of height $20m$. The walls are at distances of $30m$ and $170m$ respectively from the point of projection. Find the angle of projection.

• A. ${\tan }^{-1}\left(\frac{2}{3}\right)$
• B. ${\tan }^{-1}\left(\frac{40}{51}\right)$
• C. ${\tan }^{-1}\left(1\right)$
• D. ${\tan }^{-1}\left(\frac{4}{5}\right)$

Answer 1

The correct option is B ${\tan }^{-1}\left(\frac{40}{51}\right)$

Diagram below illustrates the situation given in the question.


$\Rightarrow$ Range, $R=200m$
By equation of trajectory of a projectile, we know
$y=x\tan \theta (1-\frac{x}{R})$
For a point $(30,20)$ we get
$20=30\tan \theta (1-\frac{30}{200})\Rightarrow \tan \theta =\frac{2}{3}\times \frac{20}{17}=\frac{40}{51}$
$\theta ={\tan }^{-1}\left(\frac{40}{51}\right)$