Question

A spaceship is 1600 m long when it is at rest. When it is traveling at a certain constant speed its length is measured by external observers and it is found to be 1100 m.

A)What is the speed of the spaceship in terms of the speed of light?

B)In the kitchen of the spaceship the chef sets the oven timer for 1.75 hours to make roast beef. How much time does the roast beef spend in the oven when measured by external observers at rest?

Answer 1

(A)

Le: Earth length = 1600

Ls: Ship Length = 1100

Ls = Le * sq rt (1 - V^2)

1100 = 1600 * sq rt (1 - V^2)

sq rt (1 - V^2 ) = 1100/1600

sq rt (1 - V^2) = 0.6875 Sq both sides

1 - V^2 = 0.47265
-V^2 = - 0.5273 Multi by -1

V^2 = 0.5273
V= 0.72615 c ....Ans



(B)

Te = earth time

Ts = ship time = 1.75 hr

Ts = Te * sq rt (1 - 0.72615^2)

1.75 hr = Te * sq rt (1 - 0.5273)
1.7 = Te * sq rt ( 0.4727)
1.7 = Te * 0.68753
Te = 2.545 hr..Ans.

Hope it will help you.

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