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 $(3m,4m)$ and $(4m,3m)$ during its motion then the range of the particle would be: $\left(g=10m{s}^{-2}\right)$

• A. $36m$
• B. $\frac{37}{7}m$
• C. $4m$
• D. $16m$

Answer 1

Answer: (B)

Using equation of trajectory:
$y=xtan\alpha \left(1-\frac{x}{R}\right)$ ;
For points $(3,4)$
$\Rightarrow 4=3tan\alpha \left(1-\frac{3}{R}\right)$ ...(i)
For point $(4,3)$
$\Rightarrow 3=4tan\alpha \left(1-\frac{4}{R}\right)$ ...(ii)
Dividing (i) and (ii)
$\Rightarrow \frac{4}{3}=\frac{3}{4}\frac{\left(1-\frac{3}{R}\right)}{1-\frac{4}{R}}\Rightarrow 16\left(1-\frac{4}{R}\right)=9\left(1-\frac{3}{R}\right)$
$\Rightarrow 7=\frac{64}{R}-\frac{27}{R}\Rightarrow R=\frac{37}{7}m$