Introduction / Context:
Here we have a speed given in kilometres per hour for a missile, and we must find the distance it travels in just one second, expressed in metres. This involves a unit conversion from km/h to m/s and then an application of the distance formula. Such questions help strengthen your ability to move between different units of speed and time, which is vital for both exams and practical problem solving.
Given Data / Assumptions:
- Speed of the missile = 1422 km/h.
- Time interval = 1 second.
- We must find the distance covered in metres during this one second.
- The missile's speed is constant over this short time.
Concept / Approach:
We use two key ideas:
1) Convert speed from km/h to m/s.
2) distance = speed * time.
The standard conversion factor is:
1 km/h = 5 / 18 m/s.
Step-by-Step Solution:
Step 1: Convert 1422 km/h to m/s.
Speed (m/s) = 1422 * (5 / 18).
First compute 1422 / 18.
18 * 79 = 1422, so 1422 / 18 = 79.
Then multiply by 5: 79 * 5 = 395 m/s.
So the missile travels 395 metres every second.
Step 2: Find the distance travelled in 1 second.
time = 1 second.
distance = speed * time = 395 * 1 = 395 m.
Therefore, the missile travels 395 m in one second.
Verification / Alternative check:
We can confirm by converting back to km/h. If the missile covers 395 m in 1 second, then per hour (3600 seconds) it will cover:
395 * 3600 = 1,422,000 m = 1422 km.
This is exactly the given speed in km/h, so our conversion is correct. That confirms the answer.
Why Other Options Are Wrong:
400 m would correspond to 1440 km/h when converted back, which is slightly higher than the given speed.
364 m or 360 m correspond to slower speeds than 1422 km/h.
319 m is also too small and gives a significantly lower speed than 1422 km/h.
Only 395 m matches a speed of 1422 km/h exactly.
Common Pitfalls:
Some students accidentally use 18 / 5 instead of 5 / 18 when converting km/h to m/s, which inverts the speed. Others mix up metres and kilometres, dividing by 3600 and 1000 in the wrong order. Rounding the conversion too early can also introduce small differences. The safest approach is to do the division 1422 / 18 exactly and then multiply by 5, making sure units are consistently handled.
Final Answer:
The missile travels
395 m in one second at a speed of 1422 km/h.
Discussion & Comments