To solve this problem, we analyze the situation step by step:

Given:

1. The distance of the car from the cyclist when it honked: $d = 1200 \, \text{m}$
2. The speed of sound: $v_{\text{sound}} = 340 \, \text{m/s}$
3. The time after which the car passes the cyclist: $t_{\text{pass}} = 30 \, \text{s}$

Step 1: Time for the sound to reach the cyclist

The time $t_{\text{sound}}$ for the sound of the horn to reach the cyclist is given by: $t_{\text{sound}} = \frac{d}{v_{\text{sound}}} = \frac{1200}{340} \approx 3.53 \, \text{s}$

Step 2: Time taken by the car to reach the cyclist

The car passes the cyclist after 30 seconds, which means the car took $t_{\text{car}} = 30 - t_{\text{sound}}$ to travel the distance of 1200 meters: $t_{\text{car}} = 30 - 3.53 \approx 26.47 \, \text{s}$

Step 3: Speed of the car

The speed of the car $v_{\text{car}}$ can now be calculated using the formula: $v_{\text{car}} = \frac{\text{distance}}{\text{time}} = \frac{1200}{26.47} \approx 45.33 \, \text{m/s}$

Final Answer:

The speed of the car is approximately: $\boxed{45.33 \, \text{m/s}}$

Would you like further clarifications or a more detailed breakdown?

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Five Related Questions:

1. How would the speed of the car change if the cyclist was moving instead of stationary?
2. What would be the car's speed if the speed of sound were different?
3. Can we calculate the time it took for the car to reach the cyclist using a different method?
4. How does the speed of sound influence such problems in real-life scenarios?
5. Could this calculation vary if the road were not straight?

Tip: Always confirm that the time intervals are consistent and properly account for delays caused by sound propagation when solving motion problems involving sound.