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A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2?
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A student sees a jet plane flying from east to west.when the jet is se...
Guys answer given in book is (D)but according to my solution answer is(B)
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A student sees a jet plane flying from east to west.when the jet is se...
Given:
- The jet plane is flying from east to west.
- When the jet is seen just above the student's head, the sound of the jet appears to reach the student making an angle of 60° with the horizontal from east.
- The velocity of sound is c.
To find:
The velocity of the jet plane.
Approach:
We can use the concept of relative velocity to solve this problem. The velocity of sound is the same for both the jet plane and the student. Therefore, we can consider the student as stationary and analyze the situation from his frame of reference.
Let's consider the following scenario:
Scenario 1: Jet Plane moving at velocity v
In this scenario, the angle at which the sound of the jet reaches the student would be 60°. However, since the jet plane is also moving, the sound waves would appear to be coming from a different direction due to the relative motion of the student and the jet.
Scenario 2: Jet Plane moving at velocity c
In this scenario, the jet plane is moving at the same velocity as the sound. Therefore, the sound waves would appear to be coming directly from the jet plane, making an angle of 0° with the horizontal.
Now, let's analyze the situation mathematically using the concept of relative velocity.
Calculation:
Let v_jet be the velocity of the jet plane.
In scenario 1:
The velocity of sound relative to the student = c - v_jet
The velocity of sound relative to the jet plane = c - 0 = c
Using the formula of relative velocity:
tan(60°) = (c - v_jet) / c
√3 = (c - v_jet) / c
√3c = c - v_jet
v_jet = c - √3c
v_jet = c(1 - √3)
In scenario 2:
The velocity of sound relative to the student = c - c = 0
The velocity of sound relative to the jet plane = c - 0 = c
Since the sound waves would appear to be coming directly from the jet plane in scenario 2, the angle would be 0°.
Conclusion:
The velocity of the jet plane, v_jet, is given by:
v_jet = c(1 - √3)
Therefore, the correct option is (C) 2c/√3.
- The jet plane is flying from east to west.
- When the jet is seen just above the student's head, the sound of the jet appears to reach the student making an angle of 60° with the horizontal from east.
- The velocity of sound is c.
To find:
The velocity of the jet plane.
Approach:
We can use the concept of relative velocity to solve this problem. The velocity of sound is the same for both the jet plane and the student. Therefore, we can consider the student as stationary and analyze the situation from his frame of reference.
Let's consider the following scenario:
Scenario 1: Jet Plane moving at velocity v
In this scenario, the angle at which the sound of the jet reaches the student would be 60°. However, since the jet plane is also moving, the sound waves would appear to be coming from a different direction due to the relative motion of the student and the jet.
Scenario 2: Jet Plane moving at velocity c
In this scenario, the jet plane is moving at the same velocity as the sound. Therefore, the sound waves would appear to be coming directly from the jet plane, making an angle of 0° with the horizontal.
Now, let's analyze the situation mathematically using the concept of relative velocity.
Calculation:
Let v_jet be the velocity of the jet plane.
In scenario 1:
The velocity of sound relative to the student = c - v_jet
The velocity of sound relative to the jet plane = c - 0 = c
Using the formula of relative velocity:
tan(60°) = (c - v_jet) / c
√3 = (c - v_jet) / c
√3c = c - v_jet
v_jet = c - √3c
v_jet = c(1 - √3)
In scenario 2:
The velocity of sound relative to the student = c - c = 0
The velocity of sound relative to the jet plane = c - 0 = c
Since the sound waves would appear to be coming directly from the jet plane in scenario 2, the angle would be 0°.
Conclusion:
The velocity of the jet plane, v_jet, is given by:
v_jet = c(1 - √3)
Therefore, the correct option is (C) 2c/√3.
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A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2?
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A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2?.
A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student sees a jet plane flying from east to west.when the jet is seen just above his head the sound of jet appears to reach him making an angle of 60•with horizantal from east.if the velocity of sound is c,then that of the jet plane is: OPTIONS (A) 2c (B)root3c/2 (C)2c/root3 (D)c/2?.
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