Question

An object is projected with a velocity of $20m/s$ 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 $A:B$ is $\left(g=10m{s}^{-2}\right)$

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

Answer 1

Answer: (D)

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 $\frac{A}{B}=\frac{\tan \theta \times 2u^2{\cos }^2\theta }{g}=40$
(As $\theta =45^{\circ },u=20m/s,g=10m/s^2)$