Question

An object is projected with a velocity of $20\text{m/s}$ making an angle of ${45}^{\circ }$ with horizontal. The equation for the trajectory is $h=Ax-B{x}^2$ where $h$ is height, $x$ is horizontal distance, A and B are constants. The ratio A : B has value of $(g=10m{s}^{-2})$

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

Answer 1

The correct option is D $40:1$

Standard equation of projectile motion
$y=x\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta }$
Comparing with given equation
$A=\tan \theta$ and $B=\frac{g}{2u^2{\cos }^2\theta }$
So $\frac{A}{B}=\frac{\tan \theta \times 2u^2{\cos }^2\theta }{g}=\frac{u^2\sin 2\theta }{g}=\frac{400}{10}=40$
$(\text{As}\theta ={45}^{\circ },u=20m/s,g=10m/s^2)$