What is the velocity ratio of an inclined plane inclined at an angle of \(30^{\circ}\) to the vertical?
A. 2 B. \(\frac{\sqrt{3}}{2}\) C. \(\frac{2 \sqrt{3}}{2}\) D. \(\frac{2 \sqrt{3}}{3}\)
Correct Answer: D
Explanation
Horizontal Since the inclined plane is inclined at \(30^{\circ}\) to the vertical, then the required angle to the horizontal is \(90^{\circ}-30^{\circ}=60^{\circ}\). See diagram above. Therefore \(V \cdot R=\frac{1}{\sin \theta} ; V R=\frac{1}{\sin 60}=\frac{1}{\frac{\sqrt{3}}{2}}\) \(=1 \times \frac{2}{\sqrt{3}}: V R=\frac{2}{\sqrt{3}}\) by rationalization \(V R=\frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} ; V R=\frac{2 \sqrt{3}}{3}\)EWARE of option A which is 2. This is what you get when Jou use \(\theta\) as \(30^{\circ}\)