Question: A captain is on a routine patrol a few thousand kilometers away from his home space station, where the origin of a three dimensional coordinate system is located (distances expressed in kilometers). Looking for action he grins as he spots an enemy ship. His display monitor shows that his position is . He hits the attack button on his computer, and his ship begins to travel, starting at , along attack curve , where t is in seconds, firing off a projectile at the enemy at t=2 seconds. The projectile travels along a straight line having the same direction as the captain’s velocity vector at t=2, with a constant acceleration of 4 km/s ² . The projectile has an initial speed which is 45 km/s faster than the ship’s speed at the firing time.

Unfortunately, the captain’s computer makes a mistake, and it programs the projectile to explode prematurely at 4 seconds after being fired. When the projectile explodes, it will annihilate everything within a 100 km radius, and in the meantime, the captain has no choice but to continue along the same attack curve for another 5 seconds, before he regains control of his ship. Will he make it? How far from the projectile will he be when it explodes?

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