Chapter 2 - One-Dimensional Kinematics - Problems and Conceptual Exercises - Page 54: 82

Bill: $x=(4.905~m/s^2)t^2$ Ted: $x=2~m-(4.2~m/s)t+(4.905~m/s^2)t^2$

$x=x_0+v_0t+\frac{1}{2}at^2$ Bill: $x_0=0$, $v_0=0$, $a=g=9.81~m/s^2$ $x=0+0t+\frac{1}{2}(9.81~m/s^2)t^2$ $x=(4.905~m/s^2)t^2$ Ted: $x_0=2~m$, $v_0=-4.2~m/s$, $a=g=9.81~m/s^2$ $x=2~m+(-4.2~m/s)t+\frac{1}{2}(9.81~m/s^2)t^2$ $x=2~m-(4.2~m/s)t+(4.905~m/s^2)t^2$