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Repeat the falling parachutist problem (Example 1.2 ), but with the upward force due to drag as a second-order rate: \[ F_{u}=-c v^{2} \] where $c=0.225 \mathrm{kg}...

Question

Repeat the falling parachutist problem (Example 1.2 ), but with the upward force due to drag as a second-order rate: \[ F_{u}=-c v^{2} \] where $c=0.225 \mathrm{kg} / \mathrm{m} .$ Solve for $t=0$ to $30,$ plot your results, and compare with those of Example 1.2.

Repeat the falling parachutist problem (Example 1.2 ), but with the upward force due to drag as a second-order rate: \[ F_{u}=-c v^{2} \] where $c=0.225 \mathrm{kg} / \mathrm{m} .$ Solve for $t=0$ to $30,$ plot your results, and compare with those of Example 1.2.



Answers

Free Fall. In Section 2.1, we discussed a model for an object falling toward Earth. Assuming that only air resistance and gravity are acting on the object, we found that the velocity $ \boldsymbol{v} $ must satisfy the equation
$$ m \frac{d v}{d t}=m g-b v $$
where $ m $ is the mass, $ \boldsymbol{g} $ is the acceleration due to gravity, and $ b>0 $ is a constant (see Figure 2.1). If $ m=100 \mathrm{kg} $, $ g=9.8 \mathrm{m} / \mathrm{sec}^{2}, b=5 \mathrm{kg} / \mathrm{sec} $ and $ v(0)=10 \mathrm{m} / \mathrm{sec} $, solve for $ v(t) $. What is the limiting (i.e., terminal) velocity of the object?


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