Consider the acceleration due to gravity, g, at a height h above the surface of a planet of mass m.
(a) If m is held constant, is g an increasing or decreasing function of h? Why?
(b) if h is held constant, is g an increasing or decreasing function of m? Why?
My ideas
(a) g = f(h,m)
I would guess h.
(b) same equation. I'd guess yes as well.
Both factors seem equally involved in making the function decreasing or increasing.
I don't know how to solve these without guessing, though.
Thanks!
I suspect you have completely misunderstood the question since this doesn't even makes sense. You answer must be one of "increasing", "decreasing", or "neither". In any case, as mr fantastic suggests, this is really a question of your knowledge of physics, not mathematics.
How does the rate at which an object falls depend upon its mass?
Now, I am confused! You did not answer "yes" before! Again, the answer must be one of "increasing", "decreasing", or "neither". How does the rate at which an object falls depend upon its mass? Again, that is a physics question, not a mathematics question. (And the answer may well depend upon how high this height is!)(b) same equation. I'd guess yes as well.
Both factors seem equally involved in making the function decreasing or increasing.
I don't know how to solve these without guessing, though.
Thanks![/QUOTE]