A Boy Stand At A Certain Distance From A Large Building And Blow A Whitle After 2.3s He Hear It Echo.He Move 50m Toward The Building And Blow He Whitle Again, This Time It Echo Reach Him After 2.0s.Calculate The(1)boy Original Distance From The Building (2)the Speed Of Sound In Air?
distanceofecho=2*distancefrombuilding
distanceofecho=vsound*time
so between the two echos...
50*2=vsound(2.3-2.0)
vsound=100m/.3sec=333 m/s
1. r *( 2.3/2) = d,
r = 0.87d.
r *( 2/2) = d-50,
Replace r with 0.87d:
0.87d * 1 = d-50,
d = 384.6 m.
2. r = 0.87d = 0.87 * 384.6 = 335 m/s.= Speed of sound.
To solve this problem, we can use the concepts of time, distance, and the speed of sound. Let's break it down step by step:
1) Boy's original distance from the building:
When the boy blows the whistle, he hears the echo after some time. Since the speed of sound is the same while going to the building and coming back, we can divide the time by 2 to calculate the time it takes for the sound to reach the building.
Therefore, the time taken for the sound to reach the building is 2.3 seconds / 2 = 1.15 seconds.
Now, we know the time it takes for the sound to reach the building, and we need to calculate the distance. We can use the formula:
Distance = Speed * Time
We rearrange this formula to solve for the distance:
Distance = (Speed of sound) * (Time taken)
Plugging in the values we have:
1.15 seconds = (Speed of sound) * (Time taken)
We'll call the speed of sound "v" and the original distance "d".
So, the equation becomes:
1.15 seconds = v * (Time taken) ---(Equation 1)
2) Boy's new distance from the building:
After the boy moves 50 meters towards the building, his new distance from the building is the original distance minus 50 meters. So the new distance is:
d - 50
Now, let's calculate the time it takes for the echo to reach the boy after he moves:
Given that the time taken is 2.0 seconds, we can use the same formula:
2.0 seconds = v * (Time taken)
Now, we can substitute the variables in this equation as well:
2.0 seconds = v * (d - 50) ---(Equation 2)
From the given information, we have two equations (Equation 1 and Equation 2) with two variables (v and d). We can solve these equations simultaneously to find the values of v and d.
Let's solve the equations:
From Equation 1, we can rearrange it to solve for v:
v = 1.15 seconds / (Time taken)
Substituting the value of 1.15 seconds and the given value of Time taken = 2.3 seconds:
v = 1.15 seconds / 2.3 seconds
v = 0.5 m/s
Now, we have the value of v. We can substitute this value into Equation 2:
2.0 seconds = 0.5 m/s * (d - 50)
We can simplify this equation further:
2.0 seconds = 0.5d - 25
Adding 25 to both sides of the equation:
2.0 seconds + 25 = 0.5d
27 = 0.5d
Dividing both sides by 0.5:
d = 27 / 0.5
d = 54 meters
Finally, we have the answer:
1) The boy's original distance from the building is 54 meters.
2) The speed of sound in air is 0.5 m/s.