Let's solve each problem step by step.

Problem 20:

Given:

• Speed of bullet: $v_b = 660 \, \text{m/s}$
• Distance to the target: $d = 200 \, \text{m}$
• Time it takes for the sound to reach the marksman: $t = 0.90 \, \text{s}$

To Find:

• Speed of sound $v_s$

Solution:

1. Time for bullet to hit the target: $t_b = \frac{d}{v_b} = \frac{200 \, \text{m}}{660 \, \text{m/s}} = 0.303 \, \text{s}$
2. Time for the sound to travel back: $t_s = t - t_b = 0.90 \, \text{s} - 0.303 \, \text{s} = 0.597 \, \text{s}$
3. Speed of sound: $v_s = \frac{d}{t_s} = \frac{200 \, \text{m}}{0.597 \, \text{s}} \approx 335.34 \, \text{m/s}$

Problem 21:

Given:

• Speed of the car: $v_c = 90.0 \, \text{m/s}$
• Distance to explosion: $d = 270.0 \, \text{m}$
• Time to hear the sound: $t = 3.8 \, \text{s}$

To Find:

• Speed of sound $v_s$

Solution:

1. Time for the car to reach the explosion point: $t_c = \frac{d}{v_c} = \frac{270.0 \, \text{m}}{90.0 \, \text{m/s}} = 3.0 \, \text{s}$
2. Time for the sound to travel back: $t_s = t - t_c = 3.8 \, \text{s} - 3.0 \, \text{s} = 0.8 \, \text{s}$
3. Speed of sound: $v_s = \frac{d}{t_s} = \frac{270.0 \, \text{m}}{0.8 \, \text{s}} = 337.5 \, \text{m/s}$

This confirms that both problems were correctly calculated, with the second problem specifically matching the given answer of $337.5 \, \text{m/s}$.

Would you like more details on any step, or do you have any further questions?

Here are 5 related questions for further practice:

1. If the speed of sound changes, how would that affect the time it takes for sound to travel the same distance?
2. How would the time delay change if the bullet speed increased in problem 20?
3. What if the car in problem 21 was moving at a slower speed? How would that impact the time $t_s$?
4. How do environmental factors, like temperature, affect the speed of sound?
5. Can you calculate the time delay in hearing a gunshot at a certain distance if the speed of sound is known?

Tip: The speed of sound is affected by factors like temperature, pressure, and the medium through which it travels. Always consider these when solving real-world problems involving sound.