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 the distance the bullets travel before the observer hears the sound, we need to calculate the time it takes for the sound to reach the observer. Let's break down the problem step by step:
Step 1: Calculate the time it takes for the sound to travel from the marksman to the observer.
The speed of sound in dry air at 20 °C is approximately 343 m/s. To calculate the time it takes for the sound to reach the observer, we use the formula:
Time = Distance / Speed
Given that the distance from the marksman to the observer is 25 m and the speed of sound is 343 m/s, we have:
Time = 25 m / 343 m/s
Calculating this, we find that it takes approximately 0.073 seconds for the sound to reach the observer.
Step 2: Calculate the distance traveled by the bullet during this time.
Since the bullet is fired horizontally and we're ignoring air resistance, the horizontal speed of the bullet remains constant at 840 m/s.
Given that the time for the sound to reach the observer is approximately 0.073 seconds and the horizontal speed of the bullet is 840 m/s, we can calculate the distance traveled by the bullet using the formula:
Distance = Speed x Time
Distance = 840 m/s x 0.073 s
Calculating this, we find that the bullet travels approximately 61.32 meters before the observer hears the sound of the rifle.