Question

As you zip through space in your PPS (personal propulsion suit), your pulse rate as you count it is 109 bpm 109 bpm (beats per minute). This high pulse rate serves as objective evidence of your excitement. However, an observer on the Moon, an expert in pulse rate telemetry, measures your pulse rate as slower. In fact, she detects only 0.587 0.587 times the rate you count and claims that you must be pretty calm in spite of everything that is going on. How fast are you moving with respect to the Moon?

Answer 1

The speed is 2.427 x10⁸ m/s

Step-by-step explanation:

The equation for measured time is the following:

`t'=xt_(o)`

Where

x = 0.587

Replacing:

`t'=0.587t_(o)`

The equation for the speed is:

`t'=\frac{t_(o) }{\sqrt{1-((v^(2) )/(c^(2) )) } } \\0.587t_(o) =\frac{t_(o) }{\sqrt{1-((v^(2) )/(c^(2) )) } }\\0.587=\sqrt{1-(v^(2) )/(c^(2) ) } \\0.587^(2) =1-(v^(2) )/(c^(2) )`

Rearrange the expression:

`0.344=1-(x^(2) )/(c^(2) ) \\v=\sqrt{0.656c^(2) } =0.809c`

Where c = 3x10⁸m/s

Replacing:

v = 0.809 * 3x10⁸ = 2.427 x10⁸ m/s