Question

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

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

Answer 1

The correct option is D $40:1$

$u=20m/s$
$\theta ={45}^{\circ }$
$h=Ax-B{x}^2\left(m\right)$
$x=range=\frac{u^{2}sin2\theta }{g}$

At the end, $h=0$
$\therefore 0=Ax-B{x}^2$
$\Rightarrow Ax=B{x}^2\Rightarrow \frac{A}{B}=x=\frac{u^{2}sin2\theta }{g}$

$\Rightarrow \frac{A}{B}=\frac{20\times 20}{10}sin{90}^{\circ }=\frac{40}{1}$