In 2286, Admiral Kirk and his crew were forced to use the sling shot effect in a
ID: 1444544 • Letter: I
Question
In 2286, Admiral Kirk and his crew were forced to use the sling shot effect in a stolen Klingon Bird-of-Prey to travel back in time to the late 20th century to retrieve two humpback whales. The stolen Klingon Bird-of-Prey traveled towards the sun at a velocity of warp 9.8 (2.94 x 109 m/s), while the sun was moving towards them at a velocity of 9 x 107 m/s, then traveled around the sun (using the sun's gravitational field) such that the stolen Klingon Bird-of-Prey was now moving in the opposite direction from whence it started, with a new velocity. Find this new velocity, assuming the mass of the sun is much larger than the mass of the spaceship.
Explanation / Answer
Here, Applying conservation of momentum
=> (1.989 x 1030 * 2.94 x 109 ) - (1.989 x 1030 * 9 x 107) = ( 5.31 * 105 + 1.989 x 1030 ) * V
=> 2.85 * 109 * 1.989 x 1030 = ( 5.31 * 105 + 1.989 x 1030 ) * V
=> V = 2.85 * 109 m/sec
=> this new velocity = 2.85 * 109 m/sec