A small ball is projected up a smooth inclined plane with an initial speed of 10 m/s along the direction at 30° to the bottom edge of the slope. It returns to the edge after 2 s. The ball is in contact with the inclined plane throughout the process. The angle of inclination is given by $\frac{π}{β}$ . Then $β$ is

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TestHub · Accepted Answer

Motion along the plane: component of gravity down the slope is $g sin θ$ ; the velocity component along the slope is $u sin 3 0^{\circ}$ .

$T = \frac{2 u s i n 3 0 ^{\circ}}{g s i n θ} = 2 \Rightarrow \frac{2 \times 10 \times \frac{1}{2}}{10 s i n θ} = 2$

$sin θ = \frac{1}{2} \Rightarrow θ = 3 0^{\circ} = \frac{π}{6}$

Answer: 6

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