Question

A particle is projected from the ground at some angle to the horizontal. (Assuming point of projection to be the origin and the horizontal and vertical directions to be the x & y-axis) the particle passes through the points $(3,4)$ and $(4,3)$ during its motion then the range of the particle would be:

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

Answer 1

Answer: (B)

$\frac{37}{7}m$

Be equation of trajectory $(y=xtan[y=xtan\alpha [1-\frac{x}{R}]]$
$4=3tan\alpha [1-\frac{3}{R}]$ ...(i)
$3=4tan\alpha [1-\frac{4}{R}]$ ...(ii)
dividing (i) & (ii)
$\frac{4}{3}=\frac{3}{4}\frac{[1-\frac{3}{R}]}{1-\frac{4}{R}}\Rightarrow 16[1-\frac{4}{R}]=9[1-\frac{3}{R}]$
$7=\frac{64}{R}-\frac{27}{R}\Rightarrow R=\frac{37}{7}$