# Thread: hard related rates problems..

1. ## hard related rates problems..

hello guys! I've just registerd. I have some trouble in my calculus class.
These are the questions
First question is not a related rate problem

If y=f(w) and w=g(x), prove
y''=(dy/dw)(d²w/dx²)+(d²y/dw²)(dw/dx)²

Second problem

A guy is waking at the rate of 5 feet per second toward the spotlight which ison a post 20 feet above the ground. The guy is 6'2". Find the rate of change of the length of the guy's shadow at that exact moment when the guy is 24 feet away from the base of the post holding the spotlight.

Thirdproblem

Maple and Main streets are straight and perpendicular to each other. A
stationary police car is located on Main Street, 1/4mile from the intersection of the two streets. A sports car, driven by Nasty Ry, approaches the intersection at the rate of 40 miles per hour. How fast is the distance between the two cars changing, and how is it changing, when the moving car is 1/8mile from the intersection.

2. Originally Posted by moonyo91
hello guys! I've just registerd. I have some trouble in my calculus class.
These are the questions
First question is not a related rate problem

If y=f(w) and w=g(x), prove
y''=(dy/dw)(d²w/dx²)+(d²y/dw²)(dw/dx)²
note that y = f(g(x))

now apply the chain rule twice. (you will have to apply the product rule the second time as well.

Second problem

A guy is waking at the rate of 5 feet per second toward the spotlight which ison a post 20 feet above the ground. The guy is 6'2". Find the rate of change of the length of the guy's shadow at that exact moment when the guy is 24 feet away from the base of the post holding the spotlight.

Thirdproblem

Maple and Main streets are straight and perpendicular to each other. A
stationary police car is located on Main Street, 1/4mile from the intersection of the two streets. A sports car, driven by Nasty Ry, approaches the intersection at the rate of 40 miles per hour. How fast is the distance between the two cars changing, and how is it changing, when the moving car is 1/8mile from the intersection.