Question

As the drawing shows, a carpenter on a space station has constructed a 30.0° ramp. A rocket moves past the space station with a relative speed of 0.549c in a direction parallel to side x. What does a person aboard the rocket measure for the angle of the ramp?

Answer 1

let x is the horizontal length and y is thevertical length.

so,

tan(theta) = y/x

tan(30) = y/x

horizontal length measured by person in the rocket,

x' = x*sqrt(1 - (v/c)^2)

= x*sqrt(1 - (0.549*c/c)^2)

= x*sqrt(1 - 0.549^2)

= 0.8358*x

let theta' is the angle measured by the person in the rocket,

tan(theta') = y/x'

tan(theta') = y/(0.8358*x)

= (y/x)/0.8358

tan(theta') = tan(30)/0.8358

tan(theta') = 0.6908

theta' = tan^-1(0.6908)

= 34.6 degrees <<<<<<<<<----------------------Answer