• Tangents to curves. We saw last time that the slope of the (tangent to the) curve is given by dividing the y-component of velocity by the x-component; this time we went further and used this to constrcut an equation of the tangent line to a given curve at a given point. We also went over parametric representation of a line in the form P+tv, where P is the vector to a given point, and v is a vector with the same slope as the line (for us the velocity vector of the curve at P).
• Estimating the later position of an object, given its position and velocity at a certain time. Basically, with just this information, the best we can do is to assume that the object maintains course and speed (i.e., constant velocity), and extrapolate from there. We discussed briefly the fact that the accuracy of this approximation depends on two factors: (1) the length of elapsed time, and (2) the "curviness" of the actual path.
• Finding horizontal and vertical tangents to curves. We observed that the tangent is horizontal when the y-component of the velocity is zero, and vertical when the x-component of velocity is zero, and used that to determine where a curve has horizontal and/or vertical tangents. (Needless to say, a plot of the curve helps out quite a bit)
• Projectile motion. We looked at an example of a launched object, and found several things about it from the parametric representation of its path: its range, maximum height, time of flight, etc.

Distributions:

•  Homework Set #4

Assignment: