== Math Problem of the Day ==

If you have a rocket traveling vertically with only the mass of its fuel to carry, with earth sea level gravity, then, how much fuel must you carry to reach a height of 1 kilometer if maintaining a newton of thrust uses up 1 gram of fuel per minute.

Bonus: show the equation with height and fuel per time are both unknowns (variables).

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My Incorrect Attempt

My solution assumes a constant mass so it's incorrect... How are you actually supposed to do this?

Find the acceleration, turns out to be a constant.

height = 0.5(a - g)t^2

1N = 0.001kg * a

(1N)z = (0.001kg)z * a

a = 1000m/s^2 regardless of fuel

So how long do we need to maintain that accel to get to 1km?

1000 = 0.5(1000-9.81)t^2

t = 1.42120173762 sec (almost sqrt2)

g = .023686696g of fuel

Doesn't seem right because by that logic I can set the fuel consumption to anything and have the same acceleration.

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🎓 Dr. Freemo 🇳🇱@freemo@qoto.orgMy Incorrect Attempt

@njha To solve this you need to use a first order differential equation :)

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