Question

An object is projected with velocity $20m{s}^{-1}$ making an angle of ${45}^o$ with horizontal. The equation for its trajectory is $h=Ax-B{x}^2$ where $h$ is the height and $x$ the horizontal distance at any instant. The ratio of constants A:B is

• A. $1:5$
• B. $5:1$
• C. $1:40$
• D. $40:1$

Answer 1

The correct option is D $40:1$

Given : $u=20m/s$ $\theta ={45}^o$

Equation of trajectory of a projectile $h=\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta }$

$⟹A=x\tan \theta$ and $B=\frac{g}{2u^2{\cos }^2\theta }$

So, $A=\tan 45=1$

$B=\frac{10}{2\times (20{)}^2\times (\cos 45{)}^2}=\frac{1}{40}$

$⟹A:B=40:1$

Option D is correct.