A slingshot propels a rubber ball horizontally from a 30 m platform at 15 m/s. approximately how far from the base of the platform will the ball land

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