Provide an Appropriate Response $\frac { \mathrm { dv } } { \mathrm { dt } } = 0$

question 46

Multiple Choice

Provide an appropriate response.
-A catamaran is running along a course with the wind providing a constant force of 30 lb. The only other force acting on the boat is resistance as the boat moves through the water. The resisting force is numerically equal to Two times the boat's speed, and the initial velocity is 1 ft/sec. What is the maximum velocity in feet per second Of the boat under this wind?

• A) The maximum velocity occurs when \(\frac { \mathrm { dv } } { \mathrm { dt } } = 0\) or \(\mathrm { v } = 12 \mathrm { ft } / \mathrm { sec }\)
• B) The maximum velocity occurs when \(\frac { \mathrm { dv } } { \mathrm { dt } } = 0\) or \(\mathrm { v } = 15 \mathrm { ft } / \mathrm { sec }\)
• C) The maximum velocity occurs when \(\frac { \mathrm { dv } } { \mathrm { dt } } = 15\) or \(\mathrm { v } = 0 \mathrm { ft } / \mathrm { sec }\)
• D) The maximum velocity occurs when \(\frac { \mathrm { dv } } { \mathrm { dt } } = 12\) or \(\mathrm { v } = 0 \mathrm { ft } / \mathrm { sec }\)

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Definitions:

Risk-free Rate

The theoretical return on an investment without any risk of financial loss, typically represented by the yields on government securities.

Put Option

A financial contract that gives the holder the right, but not the obligation, to sell a specific amount of an underlying asset at a set price within a specified timeframe.

Black-Scholes

A model used to price European options, calculating the theoretical price for derivatives based on factors like volatility, time, and the risk-free rate.

Standard Deviation

A statistical measure of the dispersion or variability of a set of values, indicating how much individual values within a data set differ from the mean or average value.