Related Rates Problem: Calculating Change in Distance of a Bird and Squirrel

[madeeeeee]

Related Rates Promlem, Please Help!

Homework Statement

A bird of prey is perched at the top of a tree that is 40 m high. The bird watches as a delectable Kingston squirrel runs away from the base of the tree at a rate of 2 m/s. What is the rate of change of the distance between the bird and the squirrel when the squirrel is 30 m from the tree?

I know:

y=height of tree so y=40 m
x=distance of base from tree so x= 30 m
d=distance from bird to squirrel
dx/dt=2m/s
dd/dt=? when squirrel is 3 m from tree

with pythag theorm: 40^2+30^2=50^2
so d= 50 m

x2 + y2 = d2
f'(x) = 2x (dx/dt) + 2y(dy/dt)=2d(dd/dt)

This is how far i have come and now i am stuck. Please help with this question. Thank you

 

[dickdick]

Homework Statement

A bird of prey is perched at the top of a tree that is 40 m high. The bird watches as a delectable Kingston squirrel runs away from the base of the tree at a rate of 2 m/s. What is the rate of change of the distance between the bird and the squirrel when the squirrel is 30 m from the tree?

I know:

y=height of tree so y=40 m
x=distance of base from tree so x= 30 m
d=distance from bird to squirrel
dx/dt=2m/s
dd/dt=? when squirrel is 3 m from tree

with pythag theorm: 40^2+30^2=50^2
so d= 50 m

x2 + y2 = d2
f'(x) = 2x (dx/dt) + 2y(dy/dt)=2d(dd/dt)

This is how far i have come and now i am stuck. Please help with this question. Thank you

Well, what's dy/dt? You've got everything else you need to solve the problem, right?

 

[madeeeeee]

actually i just solved it and i got an answer of dd/dt = 6/5 m/s

 

[dickdick]

actually i just solved it and i got an answer of dd/dt = 6/5 m/s

Hmm. Can't disagree with that. dy/dt=0, right?

 

[madeeeeee]

I have another question:
I can afford to purchase 2000 m of fencing to create three, adjacent pens for my pigs. Find the dimensions of the pig pens so the fence encloses the largest possible area.

I'm having trouble drawing the picture of what the pen looks like

 

[madeeeeee]

Hmm. Can't disagree with that. dy/dt=0, right?

yes i believe so

 

[Char. Limit]

I have another question:
I can afford to purchase 2000 m of fencing to create three, adjacent pens for my pigs. Find the dimensions of the pig pens so the fence encloses the largest possible area.

I'm having trouble drawing the picture of what the pen looks like

It should be a rectangle with 3 segments.

 

[madeeeeee]

Ok I see and what is the equation l*h(2)?

 

[dickdick]

It should be a rectangle with 3 segments.

Might be. Any particular reason to assume that? I think madeeeeee could legitimately ask for a more detailed description of the geometry to be optimized. As stated, it's pretty vague.

 

[Char. Limit]

Might be. Any particular reason to assume that? I think madeeeeee could legitimately ask for a more detailed description of the geometry to be optimized. As stated, it's pretty vague.

Well, I suppose that they could form an L-shape. Still, you have a limited amount of options.

 

[madeeeeee]

What would be the equation from the figure

 

[chiro]

I have another question:
I can afford to purchase 2000 m of fencing to create three, adjacent pens for my pigs. Find the dimensions of the pig pens so the fence encloses the largest possible area.

I'm having trouble drawing the picture of what the pen looks like

With calculus its easy to show that the biggest area with four sides is a square. If you don't believe me try setting up a sample problem setting the perimeter to sum of all sides and the area to the appropriate product and use calculus to find max,min and therefore optimal size.

With this said, I would go with Char Limits suggestion of finding the area of the square taking into account the amount of fence needed to divide the three pens. Adding this constraint you will be able to find the dimensions of the "total square" and its sub-rectangles.