Answer
a)123 m
b) v= 39.2 m/s, d=44 m
c)v=9.8 m/s, d = 118 m
d)v=20 m/s, d = 103 m (Note, speed is a scalar and cannot be negative).
Work Step by Step
We know that:
$ V_f^2 = V_0^2 +2ad$
Since the final velocity is 0, we know:
$V_0^2+2ad=0$
We substitute g, the gravitational constant, for a and simplify:
$2gd=V_0^2$
$d = V_0^2/2g$
$d = 122.5 m$
b-d) We now find the speed and altitude at given points in time. We know that the speed will be given by:
$v = v_0+at$
$v_y = v_{0y}-gt$
We then find the altitude, given the equation given above:
$V_f^2-V_0^2=2ad$
Using the answer obtained using the previous speed equation as the final speed, we find:
$ d = \frac{V_f^2-V_0^2}{-2g}$
We plug in the given values to solve for the answer.
