Difficulty: Easy
Correct Answer: 45
Explanation:
Introduction / Context:
This is another speed conversion problem involving a spaceship moving at high speed. We are given the speed in kilometres per hour and asked for the distance travelled in one fifth of a second. This tests familiarity with converting km/h to m/s and then applying the distance formula for a small time interval.
Given Data / Assumptions:
Concept / Approach:
We again use the standard conversion factor between kilometres per hour and metres per second. Once the speed is known in metres per second, the distance travelled in any number of seconds is simply speed multiplied by time. Since the time is 1/5 second, we multiply the computed m/s value by 0.2. This method is quick and reliable for all similar questions.
Step-by-Step Solution:
Verification / Alternative check:
Using the definition, in one hour the spaceship travels 810 km = 810 000 metres. In 3 600 seconds this is 810 000 metres, so per second it travels 810 000 / 3 600 = 225 metres. In 0.2 seconds the distance is 225 * 0.2 = 45 metres. This confirms the earlier calculation and shows that 45 metres is correct.
Why Other Options Are Wrong:
Option 60 metres would be the distance travelled in about 0.266 seconds at 225 m/s, not 0.2 seconds. Option 75 metres corresponds to 0.333 seconds at 225 m/s. Option 90 metres corresponds to 0.4 seconds. None of these match the exact 1/5 second interval. Only 45 metres exactly fits the relationship between speed and time given in the question.
Common Pitfalls:
Learners may misread 1/5 as 5 seconds or confuse it with 0.05. Another common error is to use 18/5 instead of 5/18 for the conversion, which yields unrealistic distances. It is also easy to mistype or miscalculate 810 * 5/18 without reducing the fraction first. Simplifying 810 / 18 to 45 before multiplying makes the arithmetic easier and clearer.
Final Answer:
The spaceship travels 45 metres in one fifth of a second.
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