Suppose a rocket ship in deep space moves with constant acceleration equal to [tex]9.8 \, \text{m/s}^2[/tex], which gives the illusion of normal gravity during the flight.

(a) If it starts from rest, how long will it take to acquire a speed one-tenth that of light, which travels at [tex]3.0 \times 10^8 \, \text{m/s}[/tex]?

(b) How far will it travel in so doing?

(a). It starts from rest, and its speed increases by 9.8 m/s every second. One tenth the speed of light is (1/10) (3 x 10⁸ m/s) = 3 x 10⁷ m/s . To reach that speed takes (3 x 10⁷ m/s) / (9.8 m/s²) = 3,061,224 seconds . That's about 35 days and 10 hours.
(b). Distance traveled = (average speed) x (time of travel) Average speed = (1/2) of (1/10 the speed of light) = 1.5 x 10⁷ m/s . Time of travel is the answer to part (a) above. Distance traveled = (1.5 x 10⁷ m/s) x (3,061,224 sec) = 4.59 x 10¹³ meters That's 45.9 billion kilometers. That's 28.5 billion miles. That's about 6.2 times the farthest distance that Pluto ever gets from the Sun.

Answered by AL2006 | 2024-06-10

The rocket ship takes approximately 3,061,224 seconds (about 35 days) to reach one-tenth the speed of light under constant acceleration of 9.8 m/s². During this time, it travels about 4.59 x 10¹³ meters, approximately 45.9 billion kilometers. This distance is equivalent to roughly 28.5 billion miles.
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Answered by AL2006 | 2024-10-01