an airplane is flying at 300 m/s(672 mi/h).How much time must elapse before a clock in the airplane and one on the ground differ by 1.00 s?
To calculate the time required before a clock in the airplane and one on the ground differ by 1.00 s, we need to use the concept of relative velocity.
Here's an explanation of how to solve the problem step by step:
1. Convert the airplane's speed from meters per second to miles per hour:
- 300 m/s = 300 * 3600/1609.344 mi/h
- ≈ 671.587 mi/h (rounded to three decimal places)
2. The relative velocity between the airplane and the ground is the difference in their speeds. Since the problem asks for the time elapsed until the clocks differ by 1.00 s, let's denote that time as 't' (in seconds).
3. The relative velocity is given by the equation: relative velocity = speed of airplane - speed of ground.
- relative velocity = 671.587 mi/h - 672 mi/h
- ≈ -0.413 mi/h (rounded to three decimal places)
4. Convert the relative velocity from miles per hour to miles per second:
- -0.413 mi/h = -0.413 / 3600 mi/s
- ≈ -0.000115 mi/s (rounded to six decimal places)
5. Now, we have the relative velocity in miles per second. The clocks will differ by 1.00 s when the relative distance traveled becomes 1.00 mile.
6. Use the formula: relative distance = relative velocity * t
- 1.00 mile = -0.000115 mi/s * t
7. Rearrange the equation to solve for 't':
- t = 1.00 mile / (-0.000115 mi/s)
- ≈ -8695.65217 s (rounded to five decimal places)
8. Take the absolute value of 't', as time cannot be negative:
- t ≈ 8695.65217 s (rounded to five decimal places)
Therefore, approximately 8695.65217 seconds (or rounded to the nearest whole number, 8696 seconds) must elapse before the clock in the airplane and the one on the ground differ by 1.00 s.
Since there are 86400 seconds and 40030 km in the earth's circumference, the plane must travel 40030/86400 km.
Assuming east-west travel at the equator.
I assume that the question is ignoring the truly minuscule relativistic effects of such a slow speed.
Also, what are the chances of having a clock on the plane which is truly in synch with its longitude? The question is poorly specified and poorly worded.