Question

A projectile is thrown so as to have a maximum possible horizontal range of $400m$. Taking the point of projection as the origin, the co-ordinates of the point where the velocity of the projectile is minimum is

• A. $(400,100)$
• B. $(200,100)$
• C. $(400,200)$
• D. $(200,200)$

Answer 1

The correct option is B $(200,100)$

For $R$ to be maximum $\sin 2\theta$ should be maximum
$\Rightarrow \sin 2\theta =1\Rightarrow 2\theta ={90}^{\circ }\Rightarrow \theta ={45}^{\circ }$
According to question
$R=\frac{u^2}{g}=400m$
We know that velocity is minimum at the highest point of projectile (i.e. $H$)
by using the relation.
$R\tan \theta =4H$
$400\tan {45}^{\circ }=4H$
$\Rightarrow H=100$

$\therefore$ Coordinates of the point where velocity is minimum is $(200,100)$