Question

A ball is projected from the bottom of an inclined plane of inclination $30^{o}$ , with a velocity of $30ms^{- 1}$ , at an angle of $30^{o}$ with the inclined plane. If $g=10ms^{- 2}$ , then the range of the ball on given inclined plane is

• A. $12m$
• B. $60m$
• C. $120m$
• D. $600m$

Answer 1

Answer: (B)

Range on incline plane,
$R = \frac{\left(2 u\right)^{2} sin \left(\alpha - \beta \right) cos \alpha }{g \left(cos\right)^{2} \beta }$
Here, $\beta = 30^{\text{ο}}$ and $\alpha = 30^{\text{ο}} + 30^{\text{ο}} = 60^{\text{ο}}$
$ \, R = \frac{2 \left(\right. 30 \left.\right)^{2} sin \left(\right. 30 ^\circ \left.\right) cos \left(\right. 60 ^\circ \left.\right)}{10 \left(cos\right)^{2} \, \left(\right. 30 ^\circ \left.\right)}$
$= \frac{2 \left(\right. 30 \left.\right)^{2} \left(\right. \frac{1}{2} \left.\right) \left(\right. \frac{1}{2} \left.\right)}{10 \left(\right. \frac{3}{4} \left.\right)}$
$= 60\text{m}$