Distance equals rate times time, right?. So, after t hours A have moved
km and B has moved km.
The distance between them is, by ol' Pythagoras,
Now, can you finish?.
Vehicle A is 25km due east of vehicle B. A moves due west at 60km/h and B moves due north at 80km/h. Find an expression for the distance of separation for the two vehicles t hours later. After how many minutes is this separation distance a minimum and what is this minimum distance?
Im really just not sure how to find the expression, but i think i know how to find at how many minutes the separation distance is minimum (differentiate the expression then make f'(x) = 0. Right?)
I found the expression for distance as d = 25 + 85x, but this is wrong. Apparently (according to my teacher) i need to use the Pythagoras theorem, so i guess that means im finding displacement and not distance.... now that i reread the question thats actually pretty obvious because its distance of separation not distance travelled. :/. oh well.
Anywho, any help in finding that expression is appreciated. Thanks.
Im unsure how to differentiate this (very new to it- just started intro-calc a couple of weeks ago) but i think im on the right track.
s = √((25-60t)² + (80t)²)
s = √(625 - 3000t + 10000t²)
s = 25 - 54.77t^(1/2) + 100t
s' = -27.58/(√t) + 100
0 = -27.58/(√t) + 100
100√t = 27.58
t = 0.075 h
t = 4.5 min
but this is wrong, the answer is double this - its 9. Im really not sure what im not getting, this question has been bugging me all night. :/
thankyou for your help