A classical mechanics problem by Kunal Gupta

Classical Mechanics Level 2

A particle of mass $m$ is thrown with a fixed velocity $v$ at an angle $\theta$ from a horizontal surface. Find the value of the angle $\theta$ at which the projectile encloses the greatest area in its complete range.

pi/4 pi/6 pi/3 pi/7

2 solutions

Kunal Gupta
Jun 27, 2014

Easy: First we know that: $\large\large y= x \tan (\theta) -\frac{gx^2}{2u^2 \cos^2(\theta)}$ Integrating $\quad$ $\large Area=\int{ydx}$ Now differentiate the area w.r.t $\theta$ and equate it to zero we get $\large\theta=\frac{\pi}{3}$