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?

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Gvb

To solve this problem, we need to consider the concept of time dilation due to relative motion between two observers.

The formula for time dilation is given by:

∆t' = ∆t * √(1 - (v^2/c^2))

Where:
∆t' is the time measured by an observer in motion (airplane clock)
∆t is the time measured by an observer at rest (ground clock)
v is the velocity of the airplane relative to the ground
c is the speed of light in a vacuum (approximately 299,792 km/s or 186,282 mi/s)

In this scenario, we want the clocks to differ by 1 second (∆t' - ∆t = 1 s). We are given the velocity of the airplane, which is 300 m/s (672 mi/h). We can convert it to meters per second as follows:

v = 300 m/s

The speed of light, c, is a constant value.

c = 299,792,458 m/s

Now we can substitute the values into the time dilation formula:

1 = ∆t * √(1 - (300^2/299,792,458^2))

Simplifying the equation further:

1 = ∆t * √(1 - (90000/897,605,916,357,644))

1 = ∆t * √(1 - 0.000000000099)

1 = ∆t * √(0.999999999901)

1 = ∆t * 0.9999999500499999

∆t ≈ 1/0.9999999500499999

∆t ≈ 1.0000000499999991 seconds

Therefore, approximately 1.0000000499999991 seconds must elapse for the airplane clock and the ground clock to differ by 1 second.

To find out how much time must elapse before the clock in the airplane and the one on the ground differ by 1.00 second, we need to consider the relative velocity between the airplane and the ground.

The relative velocity is the difference in velocity between the two reference frames, which in this case is the velocity of the airplane. Given that the airplane is flying at 300 m/s, we can assume this is its velocity relative to the ground.

Now, let's convert the velocity of the airplane from meters per second (m/s) to miles per hour (mi/h). To do this, we can use the conversion factor: 1 m/s = 2.237 mi/h.

300 m/s * 2.237 mi/h = 671.1 mi/h

Therefore, the velocity of the airplane is approximately 671.1 mi/h.

To calculate the time difference between the clocks, we divide the distance traveled by the relative velocity. Since the velocity of the airplane is constant, we can calculate the distance traveled as the product of the relative velocity and the time.

Let's assume the time taken for the clock difference is 't' seconds.

Distance traveled by the airplane = Relative velocity * time
Distance = 671.1 mi/h * t

Since the distance traveled by the airplane corresponds to a time difference of 1.00 second, we can equate the two distances:

671.1 mi/h * t = 1.00 s

To express the velocity in terms of the same time unit, we need to convert 671.1 mi/h to miles per second. Since 1 hour = 60 minutes and 1 minute = 60 seconds, we can convert to miles per second using:

671.1 mi/h * (1 h/60 min) * (1 min/60 s) = 671.1 mi/(h*60*60 s)
671.1 mi/(60*60 s) = 0.1864 mi/s

Now, the equation becomes:

0.1864 mi/s * t = 1.00 s

Simplifying the equation, we can solve for 't':

t = 1.00 s / 0.1864 mi/s

Calculating this, we find:

t ≈ 5.36 seconds

Therefore, approximately 5.36 seconds must elapse before the clock in the airplane and the one on the ground differ by 1.00 second.