Answer :
To solve this problem, we need to determine how high above the ground the hammer was dropped. We are given that the hammer hits the floor at a speed of 12 feet per second, and the acceleration due to gravity [tex]\( g \)[/tex] is 32 feet per second squared. We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed (12 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height we want to find.
First, rearrange the equation to solve for [tex]\( h \)[/tex]:
1. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. 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]\( v = 12 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second[tex]\(^2\)[/tex]
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
Calculating it step-by-step:
1. [tex]\( 12^2 = 144 \)[/tex]
2. [tex]\( 2 \times 32 = 64 \)[/tex]
3. [tex]\( h = \frac{144}{64} = 2.25 \)[/tex] feet
Therefore, the hammer was dropped from a height of 2.25 feet. So the correct answer is D. 2.25 feet.
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed (12 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height we want to find.
First, rearrange the equation to solve for [tex]\( h \)[/tex]:
1. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. 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]\( v = 12 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second[tex]\(^2\)[/tex]
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
Calculating it step-by-step:
1. [tex]\( 12^2 = 144 \)[/tex]
2. [tex]\( 2 \times 32 = 64 \)[/tex]
3. [tex]\( h = \frac{144}{64} = 2.25 \)[/tex] feet
Therefore, the hammer was dropped from a height of 2.25 feet. So the correct answer is D. 2.25 feet.
