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Answer :
To solve the problem of finding out how far above the ground the hammer was when it was dropped, we can use the given formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed of the hammer when it hits the ground, which is 8 feet per second in this case.
- [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 solve for [tex]\( h \)[/tex]. Here are the steps to do that:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by rearranging the equation:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Plug in the values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate [tex]\( 8^2 \)[/tex], which is 64.
6. Calculate [tex]\( 2 \times 32 \)[/tex], which is 64.
7. Compute [tex]\( \frac{64}{64} \)[/tex], which simplifies to 1.
Thus, the hammer was dropped from a height of 1 foot above the ground. Therefore, the correct answer is:
D. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed of the hammer when it hits the ground, which is 8 feet per second in this case.
- [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 solve for [tex]\( h \)[/tex]. Here are the steps to do that:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by rearranging the equation:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Plug in the values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate [tex]\( 8^2 \)[/tex], which is 64.
6. Calculate [tex]\( 2 \times 32 \)[/tex], which is 64.
7. Compute [tex]\( \frac{64}{64} \)[/tex], which simplifies to 1.
Thus, the hammer was dropped from a height of 1 foot above the ground. Therefore, the correct answer is:
D. 1.0 foot
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