To determine the height \( h_0 \) above the ground where the acorn was before it fell, we need to find out where the acorn started falling from, given that it takes 0.216 seconds to pass the length of the meter stick. 
Use g=9.81m/s^2 for the gravitational acceleration. How high h0 above the ground was the acorn before it fell?


To determine the height \( h_0 \) above the ground where the acorn was before it fell, we can break the problem into two parts:

1. **Time to pass the meter stick**: The acorn takes 0.216 seconds to fall past the length of the meter stick, which is 1 meter.
2. **Gravitational acceleration**: The acorn is under the influence of gravity, so we can use the equations of motion to relate time, distance, and velocity under constant acceleration.

We can approach this problem using the kinematic equations of motion. Specifically, the equation for displacement under constant acceleration is:

\[
d = v_0 t + \frac{1}{2} g t^2
\]

Here:
- \( d = 1 \, \text{m} \) (the distance the acorn falls in 0.216 seconds),
- \( g = 9.81 \, \text{m/s}^2 \) (gravitational acceleration),
- \( t = 0.216 \, \text{seconds} \) (time to fall 1 meter),
- \( v_0 \) is the velocity at the top of the meter stick (the velocity after falling from the unknown height \( h_0 \)).

To find \( v_0 \), we use the relation between velocity and height:

\[
v_0 = \sqrt{2 g h_0}
\]

We substitute \( v_0 \) into the kinematic equation and solve for \( h_0 \). Let's proceed with the calculations.The height \( h_0 \) above the ground from which the acorn started to fall is approximately \( 0.65 \, \text{meters} \).

Would you like further details or clarifications on any part of the solution?

Here are 5 related questions for further practice:
1. How would the height change if the time to pass the meter stick were doubled?
2. What if the acceleration due to gravity was 1/2 of its current value?
3. How much time would it take the acorn to fall 2 meters?
4. How fast would the acorn be moving after falling 0.65 meters?
5. How would the problem change if air resistance were considered?

**Tip:** When dealing with free fall problems, always start by identifying the known values and using kinematic equations to find the unknown variables.

To determine the height h_0 above the ground where the acorn was before it fell, we need to find out where the acorn started falling from, given that it takes 0.216 seconds to pass the length of the meter stick. Use g=9.81m/s^2 for the gravitational acceleration. How high h0 above the ground was the acorn before it fell?

Learn how to determine the height from which an acorn falls using the kinematic equations of motion. This problem involves gravitational acceleration (g = 9.81 m/s^2) and the time taken to pass a meter stick (0.216 seconds). Suitable for high school students in Grades 10-12.

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