A certain freely falling object requires 1.25 s to travel the last 35.5 m before it hits the ground. From what height above the ground did it fall?

Let T be the time required to fall the entire height H. You will have to solve for both.

H = (g/2) T^2 = 4.9 T^2
H - 35.5 = (g/2)*(T-1.25)^2
= 4.9*(T-1.25)^2 = 4.9T^2 -12.25T + 7.656

Subtract the second equation from the first and solve for T. Then use that T to solve for H.

35.5 = 12.25T -7.7
T = 3.53 s

H = 60.9 m

Do it yourself and check my numbers; there could be a mistake.

To find the height from which the object fell, we can use the equations of motion for freefall.

Step 1: Identify the given information:
- Time taken to travel the last part of the distance (t) = 1.25 s
- Distance traveled in the last part (d) = 35.5 m
- Acceleration due to gravity (g) = 9.8 m/s^2 (approximately)

Step 2: Use the kinematic equation of motion to find the initial velocity (u) in the last part:
- d = ut + (1/2)gt^2
- Rearrange the equation to solve for u:
- u = (d - (1/2)gt^2) / t

Substituting the given values:
u = (35.5 - (1/2)(9.8)(1.25)^2) / 1.25
u = (35.5 - 7.23) / 1.25
u ≈ 24.1 m/s

Step 3: Use the kinematic equation of motion to find the initial height (h):
- v^2 = u^2 + 2gh
- Assuming the object is released from rest, the final velocity (v) is 0 m/s.
- Rearrange the equation to solve for h:
- h = (0 - u^2) / (2g)

Substituting the values:
h = (0 - (24.1)^2) / (2 * 9.8)
h = -581.21 / 19.6
h ≈ -29.68 m

The negative sign indicates that the object fell from a height of approximately 29.68 meters above the ground.

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)gt^2

Where:
h is the height above the ground,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time taken to fall.

In this case, we are given the time it takes for the object to travel the last 35.5 m before hitting the ground, which is 1.25 s. We can use this information to find the height of the fall.

Plugging the values into the equation, we have:

h = (1/2)(9.8)(1.25)^2
h = (1/2)(9.8)(1.5625)
h = 7.6245 m

Therefore, the object fell from a height of approximately 7.6245 meters above the ground.