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whiteti

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Sir Isaac Newton is 13km due north of Gottfried Wilhelm Leibniz. At 11:30am, Leibniz begins walking due west at a speed of 6km/h and Newton begins walking due south at a speed of 4km/h. At what rate is the distance between these founders of calculus changing at 1:30pm?

I haven't seen a word problem since high school, plus this isn't just a word problem its a differentiation/ derivative problem :( I'm so lost and suck at diagrams. please help!
 
How much time has passed, since you graduated from high school?
 
alright, I'll stop using this site since you seem to be out to get me. Thanks anyways.
 
whiteti said:
Sir Isaac Newton is 13km due north of Gottfried Wilhelm Leibniz. At 11:30am, Leibniz begins walking due west at a speed of 6km/h and Newton begins walking due south at a speed of 4km/h. At what rate is the distance between these founders of calculus changing at 1:30pm?

I haven't seen a word problem since high school, plus this isn't just a word problem its a differentiation/ derivative problem :( I'm so lost and suck at diagrams. please help!
Click to expand...
I will try to outline the steps.

1. Begin by drawing a graph with North up and West to the left. I would put the starting point for Newton at +13km on the y-axis, and Leibniz at the origin.
2. Where are there after 2 hours of walking?
3. What is the formula for distance between? (Pythagorean theorem) Make it a function of time.
4. differentiate both sides of the distance equation with respect to t.
5. Given dy/dt = - 4 km/h and dx/dt = - 6 km/h, evaluate ds/dt.

Show us how far you can get.
 
DrPhil said:
I will try to outline the steps.

1. Begin by drawing a graph with North up and West to the left. I would put the starting point for Newton at +13km on the y-axis, and Leibniz at the origin.
2. Where are there after 2 hours of walking?
3. What is the formula for distance between? (Pythagorean theorem) Make it a function of time.
4. differentiate both sides of the distance equation with respect to t.
5. Given dy/dt = - 4 km/h and dx/dt = - 6 km/h, evaluate ds/dt.

Show us how far you can get.
Click to expand...


I got 5 km/h ... is this correct?
 
stinajeana said:
I got 5 km/h ... is this correct?
Click to expand...
I did get a nice positive integer answer, but it wasn't 5 km/h.

A hint: work with the square of the distance rather than taking the square root,
...........and then use implicit differentiation with respect to time:

\(\displaystyle \displaystyle s^2 = x^2 + y^2\)

\(\displaystyle \displaystyle 2\ s \dfrac{ds}{dt}= \cdot \cdot \cdot \)
 
whiteti said:
alright, I'll stop using this site since you seem to be out to get me. Thanks anyways.
Click to expand...
Whiteti, no one is "out to get you". It helps us to be able to do a better job in helping others with problems when we know how much schooling one has had, how long it has been since they last had any math, the highest math course they had, etc. This way we can gear our answers accordingly.
 
DrPhil said:
I did get a nice positive integer answer, but it wasn't 5 km/h.

A hint: work with the square of the distance rather than taking the square root,
...........and then use implicit differentiation with respect to time:

\(\displaystyle \displaystyle s^2 = x^2 + y^2\)

\(\displaystyle \displaystyle 2\ s \dfrac{ds}{dt}= \cdot \cdot \cdot \)
Click to expand...

re-did it and got 4km/h :) thanks!
 
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