# Homework #3 due 9-26

Stewart Page 33 Problems 9, 10, 11, 12, 19, 20, 23-41 (odd), 61, 62

# 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

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.
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?