Question

The height (in miles) of an airplane descending from the sky is given by the function f(t)= -t^(3/2). Find the distance travelled by the plane while descending, if it takes 10 minutes to land.

Answer 1

Time is typically measured in seconds, so you should first try to turn those 10 minutes into seconds.

Answer 2

Then you should just be able to substitute that value into the formula given. Replace all instances of \(t\) with the value you get.

Answer 3

okay I got 14696.94 That doesn't look right at all.

Answer 4

I did 600^(3/2)

Answer 5

They're not asking height. They're asking distance which makes this an integral problem if I'm reading correctly.

Answer 6

yes thats correct osirisis

Answer 7

i was thinking the same as osirisis, that's why i deleted my suggestion :P

Answer 8

anyways i hope you get to solve it, gtg

Answer 9

Technically it should be \(-600^{\frac{3}{2}}\). It doesn't matter much though, the answer is correct. This will find the distance because at t=0, f(t)=0.

Answer 10

That's not a general rule, just that \(-0^{\frac{3}{2}}\) is 0

Answer 11

but that number i mentioned before isn't one of the possibilities. So there must be something missing.

Answer 12

What are the possibilities?

Answer 13

-600^(3/2)=-14696.94

Answer 14

29.54 miles
33.46 miles
36.74 miles
40.47 miles

Answer 15

In that case, perhaps using minutes would have been better, if quite unusual.
\(-10^{\frac{3}{2}}=-31.62 \: miles\) , which is much closer.

Answer 16

that still doesn't deduce which answer i should choose.

Answer 17

I'm still trying to visualize an integral approach to this. Only thing I have so far is that the distance traveled is the sum of \[\Delta h \Delta t\].

Answer 18

That kind of makes sense..

Answer 19

Sorry I'm at a loss on this one. The graph of the function is already delta h I believe as it is a steadily decreasing value. My gut says to integrate but I have no clue on limits:
\[distance=\int\limits_{?}^{?}-t^{\frac{3}{2}}dt=[-\frac{2}{5}t^{\frac{5}{2}}]_{?}^{?}\]
Issue is it doesn't give a suitable answer no matter what limits are plugged in. You may want to check again when some of the other calculus folks log in later.