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

To find out how far above the ground the hammer was when you dropped it, you can use the formula for the velocity of an object in free fall:

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

Where:
- [tex]$ v $[/tex] is the final velocity (8 feet per second in this case),
- [tex]$ g $[/tex] is the acceleration due to gravity (32 feet/second²),
- [tex]$ h $[/tex] is the height from which the object was dropped.

We want to solve for [tex]$ h $[/tex], so let's rearrange the formula to solve for [tex]$ h $[/tex]:

1. Start with the equation:

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

2. Square both sides to remove the square root:

[tex]\[ v^2 = 2gh \][/tex]

3. Solve for [tex]$ h $[/tex] by dividing both sides by [tex]$ 2g $[/tex]:

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

Now plug in the known values:

- [tex]$ v = 8 $[/tex] feet per second
- [tex]$ g = 32 $[/tex] feet/second²

4. Calculate [tex]$ h $[/tex]:

[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]

[tex]\[ h = \frac{64}{64} \][/tex]

[tex]\[ h = 1.0 \][/tex] foot

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

A. 1.0 foot