A sprinter crosses the finish line of a race. The roar of the crowd in front approaches her at a speed of 357m/s . The roar from the crowd behind her approaches at 341m/s .
A) What is the speed of the sound?
B) What is the sprinter's speed?
To answer both questions, we need to use the concept of relative velocity. The relative velocity is the difference between the velocities of two objects as observed from a given reference frame.
A) To find the speed of sound, we need to consider the difference between the two speeds at which the sound approaches the sprinter from the front and behind.
The sound approaches the sprinter from the front at a speed of 357 m/s, and from behind at a speed of 341 m/s. The speed of sound will be the average of these two values.
Speed of sound = (velocity from the front + velocity from behind) / 2
Speed of sound = (357 m/s + 341 m/s) / 2
Speed of sound = 698 m/s / 2
Speed of sound = 349 m/s
Therefore, the speed of sound is 349 m/s.
B) To find the sprinter's speed, we need to consider the difference between the speed of the sound and the velocity at which it is approaching the sprinter.
The sprinter hears the sound approaching from the front at 357 m/s and from behind at 341 m/s. Since sound travels at a speed of 349 m/s, the difference between the sprinter's speed and the speed of sound will be equal to the difference between the sound's velocities from the front and behind.
Sprinter's speed = (velocity from the front - velocity from behind) / 2
Sprinter's speed = (357 m/s - 341 m/s) / 2
Sprinter's speed = 16 m/s / 2
Sprinter's speed = 8 m/s
Therefore, the sprinter's speed is 8 m/s.