Homework 1 solutions. part 1.

The key to homework 1 was to figure out a way to solve every problem starting with just the two equations:
\(y(t) = y_o + v_o t - \frac{g}{2} t^2 \)
\(v(t) = v_o - g t \)
where \(g = 9.8 \: m/s^2 \) represents the acceleration associated with the earth's gravity,
and \(v_o\) and \(y_o\) are parameters that are given in the problem statement in the most straightforward problems.  In less straightforward problems, one of these may be unknown and you may be asked to figure it out.

Here is a particularly detailed solution to problem (2.27) that illustrates how to solve this problem using only the equation for y(t). (In this problem \(y_o\) is unknown.)  Please feel free to post comments or questions about the homework in the comments below.

The following is a solution to problem 2.21 (the last problem on HW1). This solution, which also focusses on understanding how to utilize the equation for y(t), illustrates a common sign-related error (on the left) and also shows solution with the correct sign for the quadratic equation on the right.

If you would like to see the process associated with this solution, here  is a video showing that. (in the video there are two typos: neglecting to put the denominator on the right and writing 4.7 instead of 14.7. Those were added, in orange, in the still picture above.)