Question

Реактивный самолет летит со скоростью 1000 м/с На сколько часы, находящиеся в самолете, будут отставать от часов на Земле? (Подробное решение плиз)

Answer 1

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Answer 2

Calculation of Time Difference on a Supersonic Plane

To calculate the time difference between a supersonic plane and the clocks on Earth, we need to consider the speed of the plane and the time dilation effect predicted by the theory of relativity.

Let's assume that the supersonic plane is flying at a speed of 1000 m/s relative to the Earth. We'll also assume that the plane maintains this speed throughout the flight.

According to the theory of relativity, time dilation occurs when an object is moving relative to an observer. Time dilation means that time appears to pass more slowly for the moving object compared to the observer at rest.

The formula to calculate time dilation is as follows:

Δt' = Δt * √(1 - (v^2/c^2))

Where: - Δt' is the time experienced by the moving object (in this case, the clocks on the supersonic plane) - Δt is the time experienced by the observer at rest (in this case, the clocks on Earth) - v is the velocity of the moving object (1000 m/s in this case) - c is the speed of light in a vacuum (approximately 3 x 10^8 m/s)

Let's calculate the time difference:

Δt' = Δt * √(1 - (v^2/c^2))

Substituting the values:

Δt' = Δt * √(1 - ((1000 m/s)^2 / (3 x 10^8 m/s)^2))

Simplifying the equation:

Δt' = Δt * √(1 - (1/9 x 10^4))

Δt' = Δt * √(1 - 1/90000)

Δt' = Δt * √(89999/90000)

Now, we need to determine the value of Δt, the time experienced by the observer at rest (the clocks on Earth). Since the question does not provide a specific time frame, we'll assume that Δt is equal to 1 hour.

Δt' = 1 hour * √(89999/90000)

Calculating the square root:

Δt' = 1 hour * 0.9999997222

Converting the result back to hours:

Δt' ≈ 0.9999997222 hours

Therefore, the clocks on the supersonic plane will be approximately 0.9999997222 hours (or about 59.99998333 minutes) behind the clocks on Earth.

Please note that this calculation assumes constant velocity and does not take into account other factors that may affect time dilation, such as changes in velocity or gravitational effects.