Question

A person standing on an open ground hears the sound of a jet aeroplane, coming from the north at an angle 60° with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, the speed of the plane is

a. (√3/2)v
b. 2v/√3
c. v
d. v/2

Answer 1

Using trigonometry and the properties of sine, the speed of the jet plane is found to be √3/2 times the speed of sound. This result is based on the scenario described, involving a person observing the sound coming from an angle of 60° and the plane being directly overhead.

Step-by-step explanation:

The question is asking about the speed of a jet plane based on the observation made by someone on the ground. When the person perceives the sound coming at an angle of 60° but sees the plane overhead, we can use the concept of the speed of sound and the properties of sound propagation to determine the speed of the jet plane.

To solve this, we can consider the scenario as a right-angled triangle with the ground and the path of the sound as the two sides and the trajectory of the plane as the hypotenuse. If the sound is reaching the observer at a 60° angle, we can say that the sine of that angle (which is √3/2) is equal to the opposite side over the hypotenuse (the speed of the plane over the speed of sound).

Mathematically, it can be expressed as: sin(60°) = v_plane / v_sound => v_plane = sin(60°) × v_sound => v_plane = (√3/2) × v

This corresponds to option a. (√3/2) v, which means that the speed of the plane is √3/2 times the speed of sound.