You are helping with some repairs at home. You drop a hammer, and it hits the floor at a speed of 8 feet per second. If the acceleration due to gravity [tex](g)[/tex] is 32 feet/second [tex]^2[/tex], how far above the ground [tex](h)[/tex] was the hammer when you dropped it?

Use the formula:

[tex]v = \sqrt{2gh}[/tex]

A. 16.0 feet
B. 2.0 feet
C. 8.0 feet
D. 1.0 foot

To solve the problem of finding how far above the ground the hammer was when you dropped it, we can use the formula given:

[tex]\[ v = \sqrt{2gh} \][/tex]

In this formula:
- [tex]\( v \)[/tex] is the final velocity of the hammer, which is 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.

We need to rearrange the formula to solve for [tex]\( h \)[/tex]. Let's go through the steps:

1. Start with the formula for velocity:
[tex]\[ v = \sqrt{2gh} \][/tex]

2. To solve for [tex]\( h \)[/tex], first square both sides to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]

3. Next, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]

4. Now, substitute the known values into the equation:
- [tex]\( v = 8 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet per second squared

5. Calculate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \][/tex]

Therefore, the hammer was dropped from a height of 1.0 foot above the ground. So the correct answer is:

D. 1.0 foot