UpStudy Free Solution:

To determine how far above the ground the hammer was when you dropped it, we can use the given formula:

\[v = \sqrt { 2 g h} \]

Here:

- \(v\) is the final velocity (4 feet per second)

- \(g\) is the acceleration due to gravity (32 feet per second\(^ 2\))

- \(h\) is the height above the ground

First, we square both sides of the equation to eliminate the square root:

\[v^ 2 = 2 g h\]

Next, we substitute the given values into the equation:

\[4^ 2 = 2 \cdot 32 \cdot h\]

This simplifies to:

\[16 = 64h\]

Now, we solve for \(h\):

\[h = \frac { 16} { 64} = \frac { 1} { 4} \]

Thus, the height \(h\) is 0.25 feet.

So, the correct answer is:

A. 0.25 feet

Supplemental Knowledge

In physics, the motion of objects under the influence of gravity is a fundamental concept. When an object is dropped from a height, it accelerates towards the ground due to gravity, which is typically denoted as \(g\). The formula \(v = \sqrt { 2gh} \) relates the final velocity (\(v\)) of an object in free fall to its initial height (\(h\)) above the ground and the acceleration due to gravity (\(g\)).

To solve for \(h\), we can rearrange this formula:

\[h = \frac { v^ 2} { 2g} \]

Understanding kinematic equations and principles like free fall are vital in solving real-world physics issues, but UpStudy makes the concepts simpler with clear explanations and step-by-step solutions.