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The given equation for the velocity \( V \) of a falling object is:

\[
V = \sqrt{2ah}
\]

Where:
- \( a \) is the acceleration due to gravity, which is \( 32.2 \, \text{ft/sec}^2 \),
- \( h \) is the height from which the object is dropped,
- \( V \) is the velocity.

The problem asks for the height \( h \) when the velocity \( V = 80 \, \text{ft/sec} \).

Let's solve for \( h \) by isolating \( h \) in the equation:

1. Start with the equation: 
   \[
   V = \sqrt{2ah}
   \]
   
2. Square both sides to eliminate the square root:
   \[
   V^2 = 2ah
   \]

3. Solve for \( h \):
   \[
   h = \frac{V^2}{2a}
   \]

Substitute \( V = 80 \, \text{ft/sec} \) and \( a = 32.2 \, \text{ft/sec}^2 \):

\[
h = \frac{80^2}{2 \times 32.2}
\]

Now, I'll calculate the value of \( h \).The height from which the object should be dropped for it to reach a velocity of 80 ft/sec is approximately \( 99.4 \, \text{feet} \).

The correct answer is \( \boxed{99.4 \, \text{feet}} \).

Would you like further details or have any other questions?

Here are some related questions you might find helpful:
1. How does air resistance affect the velocity of a falling object?
2. What is the formula for calculating velocity with non-constant acceleration?
3. How would the calculation change if gravity was different, say on another planet?
4. How can the energy conservation principle be used to verify this result?
5. What would the velocity be if the object was dropped from a height of 200 feet?

**Tip:** Always double-check your units when working with physics problems to ensure accuracy in your calculations.

The velocity, V, of a specific object being dropped from a particular height, h, can be found by the radical function V = √(2ah), where a represents the acceleration in ft/sec². If the acceleration due to gravity is 32.2 ft/sec², at what height should you drop an object in order for it to have a velocity of 80 ft/sec?

Learn how to calculate the height needed for an object to reach a velocity of 80 ft/sec during free fall. Using the kinematic formula V = √(2ah) and the acceleration due to gravity, this physics problem is suitable for high school students in Grades 9-11.

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