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Answer :
To find the height from which the hammer was dropped, we can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here:
- [tex]\( v \)[/tex] is the final velocity (8 feet per second).
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²).
- [tex]\( h \)[/tex] is the height above the ground (what we're trying to find).
Let's rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the given values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex], which is 64:
[tex]\[ 64 = 64h \][/tex]
4. Divide both sides by 64 to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} \][/tex]
5. Simplify the right side:
[tex]\[ h = 1 \][/tex]
Therefore, the hammer was dropped from a height of 1.0 foot. So, the correct answer is A. 1.0 foot.
[tex]\[ v = \sqrt{2gh} \][/tex]
Here:
- [tex]\( v \)[/tex] is the final velocity (8 feet per second).
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²).
- [tex]\( h \)[/tex] is the height above the ground (what we're trying to find).
Let's rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the given values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex], which is 64:
[tex]\[ 64 = 64h \][/tex]
4. Divide both sides by 64 to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} \][/tex]
5. Simplify the right side:
[tex]\[ h = 1 \][/tex]
Therefore, the hammer was dropped from a height of 1.0 foot. So, the correct answer is A. 1.0 foot.
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