A ball is dropped from a building and falls with an acceleration of magnitude 10m/s^2. The distance between floors in the building is constant. The ball takes 0.5s to fall from the 14th to the 13th floor and 0.3s to fall from the 13th floor to the 12th. What is the distance between floors?

No additional physics/forces need to be taken into consideration than what is described in the question.

the time to fall to the 14th floor is

h=1/2 g (t^2)
the time tofall tothe 13th floor is
h+d=1/2 g (t+.5)^2
the time to fall to the 12th floor is
h+2d=1/2 g (t+.8)^2
subtract the first equation from the second..

d=1/2g(t+.25) check that.
now subtract the first equation from the third
2d=1/2 (1.6t+.64)
There are a number of ways to solve these two for d, t. The easiest I think it to solve for t in the first, then put that into the second and solve for d.

check my thinking

I'm sorry if I sound a tad confused, but what does g represent? Is it the acceleration (10 m/s^2)?

To solve this problem, we need to apply the equations of motion. The equation that relates distance, initial velocity, time, and acceleration is:

d = v0t + (1/2)gt^2

where:
d is the distance traveled
v0 is the initial velocity
t is the time
g is the acceleration due to gravity

Let's assume the distance between floors is d (unknown) and the ball is at rest when it is dropped from each floor, meaning the initial velocity (v0) is zero for each fall.

From the first statement, we know that the ball takes 0.5 seconds to fall from the 14th to the 13th floor. Using the equation of motion, we can write:

d = 0*t + (1/2)*10*(0.5)^2
d = 5*0.25
d = 1.25 meters

Therefore, the distance between the 14th and 13th floor is 1.25 meters.

From the second statement, we know that the ball takes 0.3 seconds to fall from the 13th to the 12th floor. Using the equation of motion, we can write:

d = 0*t + (1/2)*10*(0.3)^2
d = 5*0.09
d = 0.45 meters

Therefore, the distance between the 13th and 12th floor is 0.45 meters.

Since the distance between floors is constant, we can assume it is the same for both falls. Therefore, the distance between floors is 1.25 meters.