# Crash landing

**Calculus**Level 2

You are plummeting at 100 meters per second towards the surface of a water covered planet in a burning spaceship. You are accelerating at 2 meters per second per second due to the planets gravity, and you are 1000 meters above the surface. Until you hit the surface of the planet, your ship loses 10 percent shielding per minute from the fact that it is currently burning. When you hit the planet, your ship will lose a percent shielding equal to a tenth of your velocity. You may engage your propulsion devices at this exact moment (and no later!) to increase or decrease your velocity by up to 10 meters per second. How much should you increase or decrease your velocity by?

Details and Assumptions: Your goal is for your ship to take a minimum of damage. The atmosphere is thin enough that air resistance is insignificant. Enter a negative number if you must decrease your velocity. Your answer must be on the interval -10 to 10. Calculators are allowed.