You wish to leave this planet. Lets say that you are able to build a spacecraft

Question

You wish to leave this planet. Lets say that you are able to build a spacecraft that is capable of traveling at one-tenth the speed of light and sustaining at maximum the stress which would result from a 20-g acceleration (g = 9.8 m/s^2). The speed of light is 3 times 10^8 m/s. (a) If you are out in space and wish to make a 90 degree turn along the path of a circle, what is the minimum turning radius required so that the ship does not break up? (b) How long will it take to make the turn in part (a)?

Explanation / Answer

a_c = v^2 / r

v = 0.1c = 3 x 10^7 m/s

20g = (3 x 10^7)^2 / r

r = (3 x 10^7)^2 / (20x 9.8)

r = 4.59 x 10^12 m

b) for 90 deg turn, spaceship will travel one-forth circle ,

distance traveled = (2 pi r ) / 4

t = d /v = (0.5 x pi x 4.59 x 10^12) / (0.3 x 10^7) = 2404280.1 sec

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