It takes a freely falling object 1.80 s to travel the last 32.00 m before it hits the ground. From how high of the ground did it fall? Assume it starts from rest.

To find the height from which the object fell, we can use the equation of motion for an object in free fall:

h = (1/2) g t^2

where:
h is the height
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken to fall

In this problem, we are given the time taken to travel the last 32.00 m before hitting the ground (t = 1.80 s). We can use this information to find the height.

First, let's plug in the known values into the equation:

h = (1/2) * (9.8 m/s^2) * (1.80 s)^2

Now we need to solve the equation:

h = (1/2) * (9.8 m/s^2) * (3.24 s^2)
h = (0.5) * (9.8 m/s^2) * (3.24 s^2)
h = 15.96 m

Therefore, the object fell from a height of approximately 15.96 meters.

V1*t + 0.5g*t^2 = 32.

V1*1.8 + 4.9*1.8^2 = 32.
1.8V1 = 32 - 15.88 = 16.12.
V1 = 9.0 m/s. = Velocity at the beginning of the last 32 m.

h = (V1^2-Vo^2)/2g + 32 =
(9^2-0)/19.6 + 32 = 36.13 m.