Vector Calculus II: Summer-2021
01 : Due 6: F 7/2

1. Sailing distance S0 4266S
   1. You sail 3 nautical miles \( 10^{\circ}\) north of west and 7 nautical miles due north.

      • Construct vectors that model the legs of your journey.

      • How far are you from where you started?

   2. Time to head back
      • Construct a vector that represents your return trip.
      • Add the three vectors you have constructed.
      • Explain why the sum is reasonable in terms a sailor can understand.
2. Bennu S0 4266S Bennu is an asteroid whose orbit can be modeled by \(0.8x^2+1.8y^2=1.5\) where \(x\) and \(y\) are in astronomical units.

   • To which asteroid group does Bennu belong?

   • Construct \(d\vec{r}\) for Bennu Cartesian coordinates.

   • Construct \(d\vec{r}\) for Bennu in polar coordinates.
   • What is \(d\vec{r}\) at Bennu's aphelion?

   • The angle between \(\vec{r}\) and \(d\vec{r}\) changes as Bennu travels its orbital path. Describe how you could calculate where the angle is smallest in measure.