related rates problem need help stat! please!! Two cars start moving from the same poin. one travels south at 60mi/h and the other travels west at 25 mi/h. at what rate is the distance between the cars increasing two hours later?

Question

anonymous · Answer

Any help on this problem would be greatly appreciated!

amistre64 · Answer

looks like a right triangle relationship to me ... how would we write this up?

amistre64 · Answer

what formula do we know that compares and relates the sides of a right triangle?

anonymous · Answer

Well I think we would use implicit differentiation but would we use a formula for right triangles?

anonymous · Answer

Do we use pythagorean theorem a^2 +b^2= c^2?

amistre64 · Answer

|dw:1383768361778:dw|

amistre64 · Answer

pythag is good

what is the derivative of:

d^2 = w^2 + s^2 ?

anonymous · Answer

i was going to say that 2 is a constant so it equals 0. but that seems incorrect would  it be 2d because of the power rule? I'm not quite sure.

amistre64 · Answer

d^2 derives to 2d d'

and the others follow suit giving us:

2d d' = 2w w' + 2s s'

we can cancel out the 2s and solve for d'

d' = (w w' + s s')/d

all these parts are known or can be easily determined now

s'=60, w'=25,  at 2 hours, w=60(2) and s=25(2),  and we can know d with pythag

amistre64 · Answer

lol, um, cancel out all the 2 parts, not "2s"  :)

anonymous · Answer

oh okay thank you once the two parts are cancelled out are you left with w=120 and s= 50 then take the square root or no?

anonymous · Answer

like what is the format of the problem from this particular point?

amistre64 · Answer

d = sqrt(120^2 + 50^2)  yes

then you have all the parts for the d' rate of change

amistre64 · Answer

$$d'=\frac{w'w+s's}{d}$$
$$d'=\frac{60(120)+25(50)}{\sqrt{120^2+50^2}}$$

anonymous · Answer

ThanK you!!!

amistre64 · Answer

youre welcome