if an acorn falls 45 feet from the top of the tree, how long will it take for the acorn to hit the ground.

Solve (1/2) g t^2 = 45 feet to get t.

g = 32.2 ft/s^2

Since this is a math question, I am surprised they did not tell you the formula to use. This is really a question about physics. They may be expecting you to use a formula with a different value of g.

The formula I gave you neglects air resistance, which would lengthen the time to fall by a small amount.

To determine the time it takes for the acorn to hit the ground, we can use a formula from physics called the "equation of motion." This equation relates the distance fallen, the initial velocity, the time, and acceleration due to gravity.

The equation is as follows:

d = ut + (1/2)gt²

Where:
- d is the distance fallen (in this case, 45 feet),
- u is the initial velocity (0, as the acorn starts from rest),
- g is the acceleration due to gravity (approximately 32.174 ft/s²),
- t is the time it takes for the acorn to fall.

Substituting the given values into the equation:

45 = 0 * t + (1/2) * 32.174 * t²

Simplifying the equation:

45 = 16.087 * t²

Dividing both sides by 16.087:

t² = 2.7935

Taking the square root of both sides:

t ≈ 1.67 seconds

Therefore, it will take approximately 1.67 seconds for the acorn to hit the ground.

To determine how long it will take for the acorn to hit the ground, we can use the equations of motion. Specifically, we can use the equation for vertical motion, which is:

h = vi * t + (1/2) * g * t^2

Where:
h is the height (45 feet, in this case)
vi is the initial vertical velocity (0, as the acorn starts from rest)
g is the acceleration due to gravity (-32.2 ft/s^2, considering downward direction)
t is the time we are trying to find

To solve for t, we need to rearrange the equation:

0 = (1/2) * g * t^2 - 45

Let's solve this equation step by step:

Step 1: Rearrange the equation
(1/2) * g * t^2 = 45

Step 2: Simplify the equation
g * t^2 = 90

Step 3: Divide both sides of the equation by g
t^2 = 90 / g

Step 4: Take the square root of both sides to solve for t
t = √(90 / g)

Using the value of g (-32.2 ft/s^2), we can evaluate the equation:

t = √(90 / -32.2) ≈ 1.34 seconds

Therefore, it will take approximately 1.34 seconds for the acorn to hit the ground.