An Object with Mass $m$ Is Dropped from Rest and We Assume That the Air

question 2

Short Answer

An object with mass $m$ is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If $s ( t )$ is the distance dropped after $t$ seconds, then the speed is $v = s ^ { t } ( t )$ and the acceleration is $a = v ^ { \prime } ( t )$ . If $g$ is the acceleration due to gravity, then the downward force on the object is $m g - c v$ , where $c$ is a positive constant, and Newton's Second Law gives $m \frac { d v } { d t } = m g - c v$ .
Find the limiting velocity.

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Definitions:

Redemption Value

The amount due to an investor once a bond or other debt instrument reaches its maturity date.

CSB

Canadian Savings Bonds, a secure savings product issued and guaranteed by the Government of Canada.

Compound-Interest

A method of calculating interest where the amount is based on the initial principal and the interest that has been accumulated in past periods.

Compounded Quarterly

Involves calculating interest on an investment by adding the accrued interest back into the principal at the end of each quarter, effectively earning interest on interest.