Faraz R. answered 02/01/15
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Ok this is what we know.
We are 4000 ft from the base. That is a constant. We also know the rocket has risen 3000 ft.
40002 + 30002 = c2 Therefore c = 5000 (Pythagorean)
Now let's look at our changes:
it is vertically changing at 6000 ft/s so that means we will have a dy/dt. It is also changing in the hypotenuse because it is rising vertically.
So we will again use this formula and derive. We know the X direction is constant
so we get 40002 + y2 = c2 We will derive
0 + 2y dy/dt = 2c dc/dt We are solving for dc/dt
2 (600) (3000) = 2(5000) dc/dt
dc/dt = 360