37 m
First, let's determine how long it takes the ball to fall 30 meters.
First, two different equations for energy. First is kinetic energy, second is gravitational potential energy. For the rubber ball, the sum of those values will be constant, with all of the energy being potential at the top, and all being kinetic at the time the ball hits.
E = 0.5 mv^2
E = mha
where
E = energy
m = mass
h = height
a = acceleration
v = velocity
Now set them equal to each other.
0.5 mv^2 = mha
Now since we're looking for time, let's replace "v" with "at" on the left hand side.
0.5 m(at)^2 = mha
Simplify:
0.5 ma^2t^2 = mha
0.5 at^2 = h
at^2 = 2h
t^2 = 2h/a
t = sqrt(2h/a)
Substitute known values and calculate
t = sqrt(6.12244898 s^2)
t = 2.474358297 s
Now determine distance traveled during that time
2.474358297 s * 15 m/s = 37.11537445 m
Finally, round to 2 significant figures, giving 37 m
