Kinematics 3 Question 3

3. A person standing on an open ground hears the sound of a jet aeroplane, coming from 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, then speed of the plane is

(a) 32v

(b) v

(c) 2v3

(d) v2

figure). The length of a chamber inside the rocket is 4m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.3ms1 relative to the rocket. At the same time, another ball is thrown in x direction with a speed of 0.2ms1 from its right end relative to the rocket. The time in seconds when the two balls hit each.

(2014 Adv.)

Analytical & Descriptive Questions

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Answer:

Correct Answer: 3. (d)

Solution:

  1. Let P1 be the position of plane at t=0, when sound waves started towards person A and P2 is the position of plane observed at time instant t as shown in the figure below.

In triangle P1P2A,

P1P2= speed of plane × time =vP×t

P1A= speed of sound × time =v×t

Now, from ΔP1P2A

cosθ= base cos60=P1P2P1A=vP×tv×t12=vPvvP=v2



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