Question

The X-15 rocket-powered plane holds the record for the fastest speed ever attained by a manned aircraft at 2020 m/s. At this speed, by how much is the 15.5 m-long aircraft length contracted? Hint: use binomial approximation. a. 1.95 m b. 0.99 m c. 3.10 m d. 1.50 m

Answer 1

The length contraction of the X-15 rocket-powered plane at its fastest speed is approximately 0.99m.

Step-by-step explanation:

To calculate the length contraction of the X-15 rocket-powered plane at its fastest speed, we can use the binomial approximation. The length contraction can be determined using the equation:

Length contraction = original length * (1 - (speed^2 / c^2))^0.5

where c is the speed of light. Plugging in the values, we get:

Length contraction = 15.5m * (1 - (2020m/s)^2 / (3 x 10^8 m/s)^2)^0.5

Calculating this gives us a length contraction of approximately 0.99m. Therefore, the answer is option b. 0.99 m.

Answer 2

The contraction of the 15.5 m-long aircraft is given as L = 3.54*10-10 m

How to solve for the contraction

The speed is 2020 m/s

The length of this given aircraft is given as 15.5 m

Find the change in length

`L_0 - L_0\sqrt{1-(v^2)/(2c^2) }`

When we put in the values we have:

`15.5 - 15.5\sqrt{1-(2020^2)/((2*3*10^8)^2) }`

= 3.5 x 10 ⁻¹⁰ m

The options presented here are not the correct options