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 D 0:0098 m/s2. Suppose this spacecraft starts fromrest at time t D 0 and simultaneously fires a projectile(straight ahead in the same direction) that travels at onetenth of the speed c D 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?

Q: Please solve all steps please

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.