A body thrown along a frictionless inclined plane of angle of inclination 30° covers a distance of 40 m along the plane. If the body is projected with the same speed at angle of 30° with the ground, it will have a range of (take g = 10 ms^-2)

Let u be the initial speed with which the body is thrown along inclined ·plane. As shown in Fig, the effective deceleration is given by

                                           a = g sin $\theta$

                                              = g sin ${30}^{\circ }$ = $\frac{g}{2}$ = 5 ms^-2 

The body stops after covering a distance, say, s along the plane, which is given by;

$-2as = 0-u^2 or u=\sqrt{2as} =\sqrt{2\times 5\times 40} = 20 m{s}^{-1}$.

A projectile projected at angle  $\theta$ = 30° with this speed will have a range of

$R =\frac{u^2 \sin 2\theta }{g}=\frac{20\times 20\times \sin {60}^{\circ }}{10}=20\sqrt{3} m$