Question

The equation of projectile is $y=ax-b{x}^2$ where $a$ and $b$ are the constants. Its horizontal range is

• A. $ab$
• B. $\frac{a}{b}$
• C. $b$
• D. $a$

Answer 1

Answer: (B)

The equation of the trajectory of a projectile motion is
$y=xtan\theta -\frac{g{x}^2}{2u^{2}co{s}^2\theta }$
$y=xtan\theta \left(1-\frac{gx}{u^{2}2tan\theta co{s}^2\theta }\right)$
$=xtan\theta \left(1-\frac{gx}{u^{2}sin2\theta }\right)$
$=xtan\theta \left(1-\frac{x}{R}\right)...\left(i\right)$
where $R$ is the horizontal range of the projectile From the given equation of projectile
$y=ax-b{x}^2$
$=ax\left(1-\frac{bx}{a}\right)...\left(ii\right)$
Comparing $\left(i\right)$ and $\left(ii\right)$, we get
$\frac{1}{R}=\frac{b}{a}$ or $R=\frac{a}{b}$