Supersonic jets are able to achieve maximum speeds of up to 3.0 × 10-6c. Calculate the percentage contraction in the length of a jet plane travelling at this speed.

To calculate the percentage contraction in the length of a jet plane traveling at a certain speed, we need to use the relativistic contraction formula. The formula for length contraction is:

L' = L √(1 - (v^2 / c^2))

Where:
L' = Length of the object as measured by an observer in motion
L = Original length of the object at rest
v = Velocity of the object
c = Speed of light in a vacuum

In this case, we are given:
v = 3.0 × 10^-6c (velocity of the jet)
c = Speed of light in a vacuum (approximately 3.0 × 10^8 m/s)

Now we can substitute these values into the formula and solve for the percentage contraction:

L' = L √(1 - (v^2 / c^2))
L' = L √(1 - ((3.0 × 10^-6c)^2 / c^2))
L' = L √(1 - (9.0 × 10^-12 / 9.0 × 10^16))
L' = L √(1 - (10^-28 / 10^16))
L' = L √(1 - 10^-44)

Since the percentage contraction is defined as:

Percentage Contraction = ((L - L') / L) * 100

We can substitute the values to calculate the percentage contraction:

Percentage Contraction = ((L - L') / L) * 100
Percentage Contraction = ((L - L √(1 - 10^-44)) / L) * 100

Calculating the exact percentage contraction would require the initial length of the jet plane to be known. However, since we don't have that information, we can still solve for an approximate value using the given values.

For example, assuming the initial length L is 10 meters, we can calculate the approximate percentage contraction as follows:

Percentage Contraction = ((L - L √(1 - 10^-44)) / L) * 100
Percentage Contraction = ((10 - 10 √(1 - 10^-44)) / 10) * 100

Now, you can substitute the value for L and calculate the approximate percentage contraction.