Arthur Clarke’s The Wind from the Sun (1963) describes

Chapter 1, Problem 43P

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QUESTION:

Arthur Clarke’s The Wind from the Sun (1963) describes Diana, a spacecraft propelled by the solar wind. Its aluminized sail provides it with a constant acceleration of 0.001g = 0.0098 m/s2. Suppose this spacecraft starts from rest at time t = 0 and simultaneously fires a projectile (straight ahead in the same direction) that travels at one-tenth of the speed c = 3 × 108 m/s of light. How long will it take the spacecraft to catch up with the projectile, and how far will it have traveled by then?

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QUESTION:

Arthur Clarke’s The Wind from the Sun (1963) describes Diana, a spacecraft propelled by the solar wind. Its aluminized sail provides it with a constant acceleration of 0.001g = 0.0098 m/s2. Suppose this spacecraft starts from rest at time t = 0 and simultaneously fires a projectile (straight ahead in the same direction) that travels at one-tenth of the speed c = 3 × 108 m/s of light. How long will it take the spacecraft to catch up with the projectile, and how far will it have traveled by then?

ANSWER:

SOLUTIONStep 1Here, we have to find the time and the distance the spacecraft takes to catch up with the projectile.

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