Question

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

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

Answer 1

Answer: (D)

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