Question

A ball is projected from the bottom of an inclined plane of inclination $30^o$ , with a velocity of $30m{s}^{-1}$ , at an angle of $30^o$ with the inclined plane. If $g=10m{s}^{-2}$ , 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,
$R=\frac{{\left(2u\right)}^{2}sin\left(\alpha -\beta \right)cos\alpha }{g{\left(cos\right)}^2\beta }$
Here, $\beta =30^{\text{ο}}$ and $\alpha =30^{\text{ο}}+30^{\text{ο}}=60^{\text{ο}}$
$R=\frac{2(30{)}^{2}sin(30^{\circ })cos(60^{\circ })}{10{\left(cos\right)}^2(30^{\circ })}$
$=\frac{2(30{)}^2(\frac{1}{2})(\frac{1}{2})}{10(\frac{3}{4})}$
$=60\text{m}$