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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, given the speed it hits the ground and the acceleration due to gravity. We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity of the hammer when it hits the ground, which is 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We want to solve for [tex]\( h \)[/tex]. Start by squaring both sides of the equation to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
Now, plug in the known values:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
This simplifies to:
[tex]\[ 64 = 64h \][/tex]
To find [tex]\( h \)[/tex], divide both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \][/tex]
So, the hammer was dropped from a height of 1.0 foot above the ground. Therefore, the correct answer is:
B. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity of the hammer when it hits the ground, which is 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We want to solve for [tex]\( h \)[/tex]. Start by squaring both sides of the equation to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
Now, plug in the known values:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
This simplifies to:
[tex]\[ 64 = 64h \][/tex]
To find [tex]\( h \)[/tex], divide both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \][/tex]
So, the hammer was dropped from a height of 1.0 foot above the ground. Therefore, the correct answer is:
B. 1.0 foot
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