Question

The equation of projectile is $y = ax - bx^2$ 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)

$\frac{a}{b}$

Answer 2

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