A rocket traveled 100 km at an average speed of 28,440 km/h.
Work out how long it took the rocket to travel the 100 km. Give your answer in seconds, correct to the nearest second.
The Correct Answer and Explanation is:
The rocket took approximately 13 seconds to travel 100 kilometers at an average speed of 28,440 kilometers per hour.
Explanation
To determine how long it took for the rocket to travel a distance of 100 kilometers at a speed of 28,440 kilometers per hour, we can use the fundamental formula for calculating time when distance and speed are known:
[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
]
Here, the distance traveled by the rocket is given as 100 kilometers, and the average speed is provided as 28,440 kilometers per hour.
Step 1: Calculate Time in Hours
We start by substituting the given values into the formula:
[
\text{Time (in hours)} = \frac{100 \text{ km}}{28,440 \text{ km/h}} \approx 0.003511 \text{ hours}
]
Step 2: Convert Time to Seconds
Since time in hours is not practical for short intervals like this one, we convert it to seconds. Knowing that there are 3,600 seconds in one hour, we perform the conversion:
[
\text{Time (in seconds)} = 0.003511 \text{ hours} \times 3600 \text{ seconds/hour} \approx 12.634 \text{ seconds}
]
Step 3: Round to the Nearest Second
Finally, we round this result to the nearest whole second. Rounding 12.634 seconds gives us 13 seconds.
This calculation highlights the importance of unit conversions and understanding the relationship between distance, speed, and time. When dealing with high speeds such as those of rockets, even a relatively short distance can be covered in just a few seconds, illustrating the remarkable efficiency and speed of modern spacecraft.