Question

The trajectory of a projectile launched from ground
is given by the equation y = (- 0.025x^2 + 0.5x);
where x and y are the coordinates of the projectile
on a rectangular system of axes. Find the angle at
which projectile is launched ?
(1) 0 = tan-(0.2)
(2) A = tan-'(0.4)
(3) 0 = tan-(0.5)
(4) 0 = tan-(0.6)​

Answer 1

The standard equation of a trajectory is,

$\displaystyle\longrightarrow\sf{y=x\tan\theta-\dfrac{\tan\theta}{R}\ x^2}$

Given equation is,

$\displaystyle\longrightarrow\sf{y=0.5x-0.025x^2}$

Comparing it with the standard one, we get,

$\displaystyle\longrightarrow\sf{\tan\theta=0.5}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\theta=\tan^{-1}(0.5)}}}$

Hence (3) is the right answer.