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Answer :
To find out how far above the ground the hammer was dropped, you can use the formula for the final velocity of an object in free fall:
[tex]\[ v = \sqrt{2 \times g \times h} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final speed of the object (8 feet per second in this case).
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²).
- [tex]\( h \)[/tex] is the height from which the object was dropped.
We want to solve for [tex]\( h \)[/tex], so we need to rearrange the formula:
[tex]\[ v = \sqrt{2 \times g \times h} \][/tex]
First, square both sides to get rid of the square root:
[tex]\[ v^2 = 2 \times g \times h \][/tex]
Now, solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2 \times g} \][/tex]
Plug in the known values:
- [tex]\( v = 8 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1 \][/tex]
So, the hammer was dropped from a height of 1.0 foot above the ground. The answer is:
D. 1.0 foot
[tex]\[ v = \sqrt{2 \times g \times h} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final speed of the object (8 feet per second in this case).
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²).
- [tex]\( h \)[/tex] is the height from which the object was dropped.
We want to solve for [tex]\( h \)[/tex], so we need to rearrange the formula:
[tex]\[ v = \sqrt{2 \times g \times h} \][/tex]
First, square both sides to get rid of the square root:
[tex]\[ v^2 = 2 \times g \times h \][/tex]
Now, solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2 \times g} \][/tex]
Plug in the known values:
- [tex]\( v = 8 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1 \][/tex]
So, the hammer was dropped from a height of 1.0 foot above the ground. The answer is:
D. 1.0 foot
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