# Related Rates

(A poignant problem) A 3-foot-tall observer holds a balloon 1 foot in front of her face. Experimentally, the observer releases the balloon and watches as it rises vertically at 5 feet per second. 2 seconds after releasing the the balloon, the observer realizes that the balloon is gone forever. Find the rate of change of the angle of elevation of the observer's head at this moment.

I'm really having problems setting the example up, can you please list and label the variables also.

1. 👍 0
2. 👎 0
3. 👁 107
1. tanTheta= h/1 where h is 3ft(at t=0)
d/dt (tanTheta)=1/1ft*dh/dt
sec^2 (Theta) dTheta/dt=dh/dt

Now, at t=2, tanTheta=10ft/1=10
sec^2 Theta(dTheta/dt)=1/ft*dh/dt
dh/dt=5,
so at t=2, then secTheta=1/sqrt(1^2+10^2)=1/sqrt101
sec^2 theta=1/101

yep, the balloon is lost.
check my work

1. 👍 0
2. 👎 0

## Similar Questions

1. ### pre algebra

A company is making two types of aluminum containers. One is a cylinder with a height of 1.25 feet and a diameter of 1 foot. The other is a rectangular prism with a length of 0.75 foot, a width of 0.75 foot, and a height of 1

asked by amy on May 30, 2012
2. ### pre algebra

A company is making two types of aluminum containers. One is a cylinder with a height of 1.25 feet and a diameter of 1 foot. The other is a rectangular prism with a length of 0.75 foot, a width of 0.75 foot, and a height of 1

asked by amy on May 31, 2012
3. ### pre algebra help

A company is making two types of aluminum containers. One is a cylinder with a height of 1.25 feet and a diameter of 1 foot. The other is a rectangular prism with a length of 0.75 foot, a width of 0.75 foot, and a height of 1

asked by amy on May 30, 2012
4. ### Intermediate Algebra

If a 9-foot tall adult elephant casts an 18-foot shadow, how long is the shadow of the 6-foot zookeeper? Use a proportion to set up and solve an equation. Round your answer to the nearest tenth of a foot if necessary.

asked by Dora on July 12, 2015
5. ### algebra

i need help with a problem, if not fully explained then i might need help with another problem. I was given the formula for the volume of a sphere i, but i still don't know what to do. if you could explain to me thatll be great.

asked by anon on September 17, 2015
6. ### Calculus

An observer 150 feet from point C, where a weather balloon has been released. The balloon rises vertically at a rate of 8ft/sec/. At the very instant the balloon is 250 above ground how far is it from the observer? How Quickly is

asked by Peter on May 18, 2016
7. ### 8th grade pre algerbra

problem solving investigation: draw a diagram problem: kelly is using 3-inch square tiles to cover a 4-foot by 2-foot area the tiles are 0.5 inches tall if the tiles were stacked on top of each other to create a tower, how many

asked by mojo on October 21, 2010
8. ### MATH

13. A tree casts a shadow of 17 ft. The angle of elevation from the tip of the shadow to the top of the tree is 68°. To the nearest foot, what is the height of the tree? 14. The angle of depression of a diver from the boat is

asked by Karla on March 8, 2010
9. ### trig plz help

Solve. Round off your answer to the nearest foot. (The picture is not drawn to scale.) A balloon is 1500 feet above the ground. The angle of depression from the balloon to headquarters is 46°21'. How far is the headquarters from

asked by ashley on March 6, 2016
10. ### Applied Calculus

A hardware store owner chooses to enclose an 800 square foot rectangular area in front of her store so that one of the sides of the store will be used as one of the four sides of the fence. If the two sides that come out from the

asked by Trisha on April 8, 2012

More Similar Questions