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Answer :
To solve this problem, we need to find out how far above the ground the hammer was when it was dropped.
We are given:
- The speed at which the hammer hits the floor, [tex]\( v = 8 \)[/tex] feet per second.
- The acceleration due to gravity, [tex]\( g = 32 \)[/tex] feet/second[tex]\(^2\)[/tex].
We will use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here, we need to solve for [tex]\( h \)[/tex], which is the height from which the hammer was dropped.
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Solve for [tex]\( h \)[/tex] by squaring both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Rearrange the equation to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Plug in the given values:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate the values:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was dropped from a height of 1.0 foot.
The correct answer is C. 1.0 foot.
We are given:
- The speed at which the hammer hits the floor, [tex]\( v = 8 \)[/tex] feet per second.
- The acceleration due to gravity, [tex]\( g = 32 \)[/tex] feet/second[tex]\(^2\)[/tex].
We will use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here, we need to solve for [tex]\( h \)[/tex], which is the height from which the hammer was dropped.
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Solve for [tex]\( h \)[/tex] by squaring both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Rearrange the equation to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Plug in the given values:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate the values:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was dropped from a height of 1.0 foot.
The correct answer is C. 1.0 foot.
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