A space shuttle and a damaged satellite are 384 mi apart ...?

Question

The shuttle travels at 836 mi/h, and the satellite at 682 mi.h, in the same direction. How long will it take the shuttle to overtake the satellite, and in what distance?

Any help is greatly appreciated, thank you.

Answer 1

find the relative speeds
836-682 = 154mpH
384mi apart / 154 mpH = 2.49 hours
the satellite will have traveleed
2.49 hours * 682 mph = 1700 miles
shuttled travels 2.49 hours * 836 mph = 2085 miles

my calculator is broken i think... my first numbers were all wrong.

Answer 2

I'm going to assume we're moving in a straight line here and not in an orbit since you didn't specify. This makes the problem a simple relative motion problem and can be solved using

X=Xo + Vot (I'm assuming no acceleration since that was also not stated in the problem)

So for the shuttle the equation would be
X = 0 + 836t

and the satellite would be
X = 384 + 682t

The two will meet when the X's are equal so set the two equal and solve for t getting 2.48 hours

Plug this t back into one of the original equations to get a distance (X) of 2076 miles.

Answer 3

let the shuttle's position a the start be x = 0 and the satellite's be x0=384 miles. Let shuttle speed be v and satellite speed be u. Assuming we can treat this as linear motion (we really can't but you aren't given enough data to treat it as a real orbital problem), the the position of the shuttle and satellite as a function of time are, respectively:

x = v*t

x = x0+u*t

Now set tem equal to each other and solve for t

v*t = x0+ u*t
(v-u)*t = x0
t = x0/(v-u)
= 2.5 hours

The suttle travels x = v*t = 836 *2.5 = 2085 miles

Answer 4

so it is catching up at (836-682)=154mi/h
so 384/154=2.49
so just about 2 1/2 hours