Homework #14 due 12-1

Stewart p. 128 #17, 25, 39, 41, 57, 62, 66, 67; p. 129 #71, p. 135 #39

Advertisements

Classwork 9-23

The speed that a sailboat is capable of sailing is determined by three factors: its total length L, the surface area A of its sails, and its displacement V. In general, a sailboat is capable of greater speed if it is longer, has a larger sail area, or displaces less water. To make sailing races fair, only boats in the same “class” can qualify to race together. For a certain race a boat is considered to qualify if 0.30L+0.38A^\frac{1}{2}-3V^\frac{1}{3}\leq 16 where L is measured in feet, A in square feet, and V in cubic feet. Use this inequality to answer the following questions:
1. A sailboat has length 60 feet, sail area 3400 square feet, and displacement 650 cubic feet. Does this boat qualify for the race?
2. A sailboat has length 65 feet and displaces 600 cubic feet. What is the largest possible sail area that could be used and still allow the boat to qualify for this race?

Warp Speed and Relativity

Let’s start with some videos!

The theory of relativity states that as an object travels with velocity v, its rest mass m_0 changes to a mass m given by the formula m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} where c is the speed of light.

By what factor is the rest mass of a spaceship multiplied if the ship travels at one-tenth the speed of light?

By what factor is the rest mass of a spaceship multiplied if the ship travels at one-half the speed of light?

By what factor is the rest mass of a spaceship multiplied if the ship travels at 90% the speed of light?

Warp speed is defined by the equation v=w^3 c. If an object’s mass is twice its rest mass, what¬†warp is it travelling at?

Use the relativistic mass formula to show that it is not possible for an object with mass to travel faster than the speed of light.