Question

I only have 30 min. can someone help me?

Answer 1

30 min for what?
an online test?

Answer 2

Two cars are approaching an intersection along different roads that are perpendicular. The first car, travelling at a rate of 30feet/second, is 100 feet from the intersection at the instant the second car crosses the intersection at 40 feet/second. Find the rate of change in the distance between the cars four seconds later

Answer 3

I have to have this packet done or else I'm really screwed because I have Calc. first period and this problem is one I'm having difficulties solving

Answer 4

Draw yourself a diagram first. Then figure out the linear equations for the position of each car as a function of time.

Then use Pythagorus theorem to write down an expression for the distance between them.

Finally, differentiate that expression to find the rate of change and evaluate it for t = 4 sec.

Answer 5

d=rt
\[d _{1}=(30 fps)\times t\]\[d _{2}=(40fps) \times t\]As pointed out by JamesJ the individual distances are at right angles the resultant distance is the hypotenuse of a right triangle.\[d=\sqrt{30^{2}t ^{2}+40^{2}t ^{2}}\]
d=50t
d'=50

JamesJ help me here is the answer 50? Where does t=4 come in? Is it constantly 50??

Answer 6

Your equations for the distance aren't exactly right. At t = 0, where are both cars? Are they both in the intersection?

Answer 7

At t = 0 they are on the same plane separated by 100 ft one car is at the intersection the other 100 ft away approaching the intersection at 30 fps.
At t =4 . both have cleared the intersection (safely) and one is 20 ft away from the intersection and the other scooting at 40 fps and traveled 160 ft. Is that the way you see it.

Answer 8

I am beginning to think that they have always been traveling at 90 degrees and the distance will be changing at a constant rate (regardless of their position on the grid)

Answer 9

This can be sooo much fun, why do I torture myself LOL

Answer 10

so, is radar right? cuz i so want to write this down but i want to know if it's the right answer

Answer 11

So for car 1, d1(t) = 30t - 100
for car 2, d2(t) = 40t

Now solve.

Answer 12

those would be the sides i plug into the Pythagorean theorem?

Answer 13

Yes. Draw yourself a diagram to convince yourself they are right.

Answer 14

ok

Answer 15

Thanks JamesJ We substitute 4 for t then it is Pythagorus theorem time.

Answer 16

i got 26000 from the P.T.

Answer 17

chely2013, I think you have it. Good luck

Answer 18

THANKS

Answer 19

How did you get 26000?

Answer 20

JamesJ said to use d1(t)=30t-100 and d2(t)=40t then plug it into P.T.

Answer 21

maybe i did this in the wrong order?

Answer 22

Did you take the square root?

Answer 23

i forgot to sqr. rt.

Answer 24

i got 161.245155

Answer 25

is that right?

Answer 26

I did too, but sure would like confirmation from JamesJ

Answer 27

same here :)

Answer 28

Oh JamesJ where are you????

Answer 29

He is busy assisting others.

Answer 30

oh well

Answer 31

I got 22.4
hope I'm wrong though....