High School

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

Answer :

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