Question

A particle is projected from ground at some angle with horizontal (Assuming point of projection to be origin and the horizontal and vertical directions to be the $x$ and $y-\text{axis }$ ) the particle passes through the points $\left(\right.3m, 4m\left.\right)$ and $\left(\right.4m,3m\left.\right)$ during its motion then the range of the particle would be: $\left(g = 10 \, \, m s^{- 2}\right)$

• A. $36m$
• B. $\frac{3 7}{7}m$
• C. $4m$
• D. $16m$

Answer 1

Answer: (B)

Using equation of trajectory:
$y=xtanα\left(1 - \frac{x}{R}\right)$ ;
For points $\left(\right.3, 4)$
$\Rightarrow 4=3tan\alpha \left(1 - \frac{3}{R}\right)$ ...(i)
For point $\left(\right.4, 3)$
$\Rightarrow 3=4tan\alpha \left(1 - \frac{4}{R}\right)$ ...(ii)
Dividing (i) and (ii)
$\Rightarrow \frac{4}{3}=\frac{3}{4}\frac{\left(1 - \frac{3}{R}\right)}{1 - \frac{4}{R}}\Rightarrow 16\left(1 - \frac{4}{R}\right)=9\left(1 - \frac{3}{R}\right)$
$\Rightarrow 7=\frac{6 4}{R}-\frac{2 7}{R}\Rightarrow R=\frac{3 7}{7}m$