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Answer :
To find out how far above the ground the hammer was when you dropped it, you can use the formula for the velocity of an object in free fall:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity (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 let's rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Start with the equation:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now plug in the known values:
- [tex]\( v = 8 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second²
4. Calculate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \][/tex] foot
Therefore, the hammer was dropped from a height of 1.0 foot above the ground. The correct answer is:
A. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity (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 let's rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Start with the equation:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now plug in the known values:
- [tex]\( v = 8 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second²
4. Calculate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \][/tex] foot
Therefore, the hammer was dropped from a height of 1.0 foot above the ground. The correct answer is:
A. 1.0 foot
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