An observer stands 25 m behind a marksman practicing at a rifle range. The marksman fires the rifle horizontally, the speed of the bullets is 840 m/s, and the air temperature is 20 °C. How far does each bullet travel before the observer hears the report of the rifle? Assume that the bullets encounter no obstacles during this interval, and ignore both air resistance and the vertical component of the bullets' motion.
To determine how far the bullet travels before the observer hears the report of the rifle, we need to calculate the time it takes for the sound to travel from the marksman to the observer.
The speed of sound in air is approximately 343 m/s at 20 °C.
First, let's find the time it takes for the sound of the rifle report to reach the observer:
Distance = Speed × Time
25 m = 343 m/s × Time
Time = 25 m / 343 m/s
Time ≈ 0.073 seconds
Now that we have the time it takes for the sound to reach the observer, we can calculate how far the bullet travels in that time.
Distance = Speed × Time
Distance = 840 m/s × 0.073 s
Distance ≈ 61.32 meters
Therefore, each bullet travels approximately 61.32 meters before the observer hears the report of the rifle.
To find the distance that each bullet travels before the observer hears the report of the rifle, we need to calculate the time it takes for the sound to reach the observer.
The speed of sound in air depends on the temperature. As the temperature is given as 20 °C, we can use the formula:
v = 331.5 + 0.6 * T
where v is the speed of sound in m/s and T is the temperature in °C.
Plugging in the temperature:
v = 331.5 + 0.6 * 20
= 331.5 + 12
= 343.5 m/s
Now, we know that the bullet travels horizontally at a speed of 840 m/s and the observer is 25 m behind the marksman.
To find the time it takes for the sound to reach the observer, we can use the formula:
Time = Distance / Speed
The distance the sound needs to travel is the same as the horizontal distance the bullet travels before reaching the observer, which is 25 m.
The speed of sound is 343.5 m/s.
So, Time = 25 m / 343.5 m/s ≈ 0.073 seconds
Now that we have the time it takes for the sound to reach the observer, we can calculate the distance traveled by the bullet during that time.
Distance = Speed * Time
Distance = 840 m/s * 0.073 s
= 61.32 m (rounded to two decimal places)
Therefore, each bullet will travel approximately 61.32 meters before the observer hears the report of the rifle.
what is the speed of sound at 20°C? If it is x m/s, then
time = distance/speed = 25/x s
bullet distance = time * speed = 25/x * 840