- Draw $\vec r(t) = (3 \cos t, 3 \sin t)$.
- Draw $\vec r(t) = (3 \cos 2t, 3 \sin 2t)$.
- Hurricane Matthew has a diameter of 28 miles. Assuming the eye is at the origin $(0,0)$, give a parametrization of the exterior edge of the hurricane.
- Sustained winds are 128 mi/hr. Modify your parametrization above so that the speed is 128 mi/hr.
- The eye of the hurricane is moving north west at a speed of 12 mi/hr. Modify your parametrization so that the center moves north west at 12 mi/hr.
- An object travels along straight lines. It's velocity is $ (0,3,4) $ for 2 seconds, and then turns so it's velocity is $ (1,2,-2) $ for 5 seconds. What is the distance traveled by the object.
- Find the arc length of the curve $\vec r(t) = (t^2, t^3)$ for $0\leq t\leq 2$.
- Consider the curve $C$ parametrized by $\vec r(t) = (3-2t^2,4t+5)$ for $-1\leq t\leq 2$.
- Draw the curve $C$.
- Find $\frac{d\vec r}{dt}$. Then state $\frac{dx}{dt}$, $\frac{dy}{dt}$, and $\frac{dy}{dx}$, all in terms of $t$.
- Give a vector equation of the tangent line to the curve at $t=1$.
- Set up a formula to compute the length of the curve.
- A wire lies along the curve $C$. The density (mass per length) of the wire at a point $(x,y)$ on the curve is given by $\delta(x,y) = y+2$. Set up an integral formula that gives the total mass of the wire.
- The wire contains charged particles. The charge density (charge per length) at a point $(x,y)$ on the curve is given by the product $q(x,y)=xy$. Set up an integral formula that gives the total charge on the wire.
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