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rpmacs · Nov 19, 2009, 03:02 PM

A rocket burns up at the rate of 2.5 tons/minute after falling out of orbit into the atmosphere. If the rocket weighed 6000 tons before reentry, express its weight w as a function of the time t, in minutes of reentry.

I believe the answer is w=2.5t

6000/2.5 2.5t/2.5 t=2400

Help please

ArcSine · Nov 19, 2009, 03:50 PM

Here's a couple of hints: First, right off the bat you can tell you need the function to equal 6,000 when t = 0. That tells you that it'll probably take shape along the lines of

w(t) = 6,000 + 'something that's zero when t is zero'

Next, that second part up there ('something that's... ') needs to serve the purpose of reducing the starting weight (the first part, 6,000) at the rate of 2.5 per t.

So now we've refined it to

w(t) = 6,000 - X

where X is some expression involving t which is zero when t is zero, AND which grows ('cause I've got a negative sign in there now) at the rate of 2.5 per t.