First slide

Projectile motion

Question

A body projected along an inclined plane of angle of inclination 30° stops after covering a distance x₁. The same body projected with the same speed stops after covering a distance x₂, if the angle of inclination of the inclined plane is increased to 60°. The ratio x₁/x₂ is

Moderate

A

1
B

$\sqrt{2}$
C

$\sqrt{3}$
D

2

Solution

Let the initial speed be u. Final speed v = 0 in both cases. The retardation for $θ_{1} = 30^{\circ}$ is $a_{1} = gsin θ_{1}$ and $θ_{2} = 60^{\circ}$ is $a_{2} = gsin θ_{2}$ . Now, using $v^{2} - u^{2} = 2 ax$ , we have
$\begin{matrix} u^{2} = 2 a_{1} x_{1} \\ = 2 a_{2} x_{2} \end{matrix}$
Thus $\frac{x_{1}}{x_{2}} = \frac{a_{2}}{a_{1}} = \frac{gsin θ_{2}}{gsin θ_{1}} = \frac{\sin 60^{\circ}}{\sin 30^{\circ}} = \sqrt{3}$
Hence the correct choice is (c).

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