a man sets his watch at noon by the sound of a factory whistle 4.8 km away. If the temperature of the air is 20 degrees C, how many seconds slow will his watch be?
d = V*t = 4800 m
t = 4800/343 = 14 s.
Well, if you want to know how many seconds slow his watch will be, I guess it's time for some funny math! Let's break it down, shall we?
First, we need to figure out the speed of sound in air at 20 degrees Celsius. Now, we could get all scientific and stuff, but hey, let's just say it moves at the speed of a snail on a lazy Sunday... or about 343 meters per second.
So, the sound travels 4.8 kilometers, which is 4800 meters. If we divide that by 343, we get approximately 14 seconds.
But wait, there's more! Because the sound needs to reach his ear before it can set his watch, we have to take that into account. Now, the average human reaction time is about 0.25 seconds. So let's add that to our calculations.
In total, his watch will be about 14.25 seconds slow. Poor guy, he'll be fashionably late for everything!
To determine how many seconds slow the watch will be, we need to calculate the time it takes for the sound of the factory whistle to reach the man. Since the speed of sound depends on the temperature of the air, we can use the formula for calculating the speed of sound:
v = 331.4 + 0.6 * T
where v is the speed of sound in m/s and T is the temperature in degrees Celsius.
First, let's convert the distance from kilometers to meters:
Distance = 4.8 km = 4.8 * 1000 = 4800 m
Now, let's calculate the speed of sound at 20 degrees Celsius:
v = 331.4 + 0.6 * 20
= 331.4 + 12
= 343.4 m/s
Next, we can calculate the time it takes for the sound to travel the distance:
Time = Distance / Speed
= 4800 m / 343.4 m/s
≈ 13.99 s
Finally, we can calculate how many seconds slow the watch will be based on the time it took for the sound to reach the man:
Seconds slow = Time - 12 (noon)
= 13.99 s - 12 s
≈ 1.99 s
Therefore, the man's watch will be approximately 1.99 seconds slow.
To determine how many seconds slow the man's watch will be, we need to consider the speed of sound and its dependence on temperature.
The speed of sound in air can be approximated by the formula:
v = 331.4 + 0.6 * T
where v is the speed of sound in meters per second and T is the temperature in degrees Celsius.
First, let's convert the distance from kilometers to meters:
Distance = 4.8 km = 4.8 * 1000 m = 4800 m
Next, we can substitute the temperature, T, in degrees Celsius:
T = 20 degrees Celsius
Using the speed of sound formula, we can calculate the speed of sound at the given temperature:
v = 331.4 + 0.6 * T
v = 331.4 + 0.6 * 20
v = 331.4 + 12
v = 343.4 m/s
Now, we can calculate the time it takes for the sound to travel 4800 meters:
Time = Distance / Speed
Time = 4800 m / 343.4 m/s
Time ≈ 14 seconds
Therefore, the man's watch will be approximately 14 seconds slow.