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Answer :
To solve this problem, we need to determine how far above the ground the hammer was when it was dropped. We know the speed of the hammer when it hits the floor is 8 feet per second, and the acceleration due to gravity is 32 feet per second squared. We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
In this formula:
- [tex]\( v \)[/tex] is the final speed 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 above the ground, which we need to find.
We need to rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ v = \sqrt{2gh} \][/tex]
First, square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
Next, solve for [tex]\( h \)[/tex] by rearranging the equation:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now substitute the known values into the equation:
- [tex]\( v = 8 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second[tex]\(^2\)[/tex]
Plug these values into the formula:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \][/tex]
The height from which the hammer was dropped is 1.0 foot. Therefore, the correct answer is:
D. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
In this formula:
- [tex]\( v \)[/tex] is the final speed 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 above the ground, which we need to find.
We need to rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ v = \sqrt{2gh} \][/tex]
First, square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
Next, solve for [tex]\( h \)[/tex] by rearranging the equation:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now substitute the known values into the equation:
- [tex]\( v = 8 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second[tex]\(^2\)[/tex]
Plug these values into the formula:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \][/tex]
The height from which the hammer was dropped is 1.0 foot. Therefore, the correct answer is:
D. 1.0 foot
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