Question

Set the ranges for following projectiles in decreasing order for same velocity of projection :
a) $\theta ={15}^0$
b) $\theta ={45}^0$
c) $\theta ={55}^0$
d) $\theta ={85}^0$

• A. d, a, c,b
• B. a,b, c, d
• C. d, c, b, a
• D. b, c, a, d

Answer 1

The correct option is D b, c, a, d

$R=\frac{v^2\sin 2\theta }{g}$
So, with $v$ & $g$ constant, $R\propto \sin 2\theta$
So, $R_1\propto \sin {30}^{\circ }=1/2$
$R_2\propto \sin {90}^{\circ }=1$
$R_3\propto \sin {110}^{\circ }=0.9396$
$R_4\propto \sin {170}^{\circ }=0.173$

Clearly, $\sin {90}^{\circ }>\sin {110}^{\circ }>\sin {30}^{\circ }>\sin {170}^{\circ }$
$b>c>a>d$