A plane which is Inclined at an angle of 30 ° to the horizontal has a velocity ratio of

Analyze the question: An inclined plane is a simple machine. We need its velocity ratio (VR) when the angle of inclination is 30°.

Concept: Velocity ratio = distance moved by the effort ÷ distance moved by the load.

For an inclined plane:

• The effort moves along the slope, so the distance is the length of the incline, l.
• The load is raised through the vertical height, h.

So:

VR = l / h = 1 / sin θ

Solution:

θ = 30°

VR = 1 / sin 30°

sin 30° = 0.5

VR = 1 / 0.5 = 2

Tip: For an inclined plane, VR = 1/sin θ. Since sin θ is never more than 1, the VR is always at least 1. A gentler slope gives a bigger VR, which means you need less effort but must move it over a longer distance. Don't confuse this with 0.5, which is just sin 30°. You must take the reciprocal.