A train is traveling at 30.0 m/sm/s relative to the ground in still air. The frequency of the note emitted by the train whistle
1 answer:
Answer
given,
speed of sound = 344 m/s
speed of train = 30 m/s
frequency emitted by the train = 262 Hz
Doppler's effect
f_L is the frequency of listener
f_S is the frequency of the source of the sound
v is the speed of the sound
v_L is the speed of listener.
v_S is the speed of the source
a) Speed of the passenger in another train , v = 18 m/s
another train is moving in opposite direction and approaching
v_L is positive as the listener is moving forward.
v_S is negative at the source is moving toward the listener.
b) Speed of the passenger in another train , v = 18 m/s
another train is moving in opposite direction and receding
v_L is negative as the listener is moving away from source.
v_S is positive at the source is moving away the listener.
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During a rodeo, a clown runs 7.7 m north, turns 49.9 degrees east of north, and runs 6.4 m. Then after waiting for the bull to come near, the clown turns due east and runs 19.8 m to exit the arena. The magnitude of the clown’s displacement is 27 m.
<u>Explanation: </u>
As the clown is running in the north direction for about 7.7 m and then he turns 49.9 degrees east of north. In the east of north, he covers a distance of 6.4 m and then turns east to exit the arena after covering a distance of 19.8 m. Let’s have a simple diagram to easily understand the problem.
In first step, the clown runs 7.7 m in north direction, so the image will be as in fig 1. Then he takes a direction of north east and covers a distance of 6.4 m, so the image will be modified as in fig 2. Then after the bull comes, he turns east and runs 19.8 m to exit the arena, so the image will be as in figure 3.
So, the extension of North line and the East line at a point shown as the dotted line in the above image, forms the total displacement as the hypotenuse of a right angled triangle. The extended dotted lines is nothing but the horizontal and vertical components of the angle 49.9 degree.
By using Pythagoras theorem, the total displacement can be found as
Similarly, the adjacent side of this imaginary triangle is the distance covered by the clown in the North direction.
Thus, the total displacement covered by the clown is
Thus, the total displacement by the clown is 27 m.
