Homework: Week #4

• Due at the start of class on Monday, September 13...

Exercises:

1. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1.3m higher than the bow of the boat. The rope is being pulled in at a rate of 2m/s and at time t=0, there is 15m of rope between the boat and the pulley. (Assume the rope always forms a straight line.) Write a function d(t) that gives the distance of the boat from the dock after t seconds have elapsed.
2. Two streets intersect at a 110 degree angle. There is a monument on one of the streets, 7mi from the intersection. If a car leaves the intersection at time t=0 and travels 30mph along the other street, write a function that gives the distance x(t) between the car and the monument at time t.
3. An extendable ladder may vary between 16 and 24 feet in length. At time t=0 the ladder is standing vertically against a wall, and fully retracted to 16ft. At that time the bottom of the ladder is pulled away from the wall at a rate of 3ft/s and simultaneously, the ladder is extended at a rate of 1ft/s.
• At what time will the top of the ladder touch the ground.
• Write a function h(t) that gives the height of the top of the ladder after t seconds.
• What is the average speed of the top of the ladder during the first second? During the last second?

• Due at the start of class on Wednesday, September 15...

Exercises:

The problems from Monday's assignment, which was not properly linked.
The additional problem from Monday's lecture.

• Due at the start of class on Friday, September 17...