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Answer :
To solve the problem of finding out how far above the ground the hammer was dropped from, we can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity at which the hammer hits the ground (4 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²),
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We need to rearrange this formula to solve for [tex]\( h \)[/tex]. Here's how you can do it step-by-step:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides of the equation to eliminate 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]
4. Substitute the known values into the equation:
- [tex]\( v = 4 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{4^2}{2 \times 32} \][/tex]
5. Calculate the value:
- [tex]\( 4^2 = 16 \)[/tex]
- [tex]\( 2 \times 32 = 64 \)[/tex]
- [tex]\( \frac{16}{64} = 0.25 \)[/tex]
The height ([tex]\( h \)[/tex]) from which the hammer was dropped is 0.25 feet above the ground.
Therefore, the correct answer is C. 0.25 feet.
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity at which the hammer hits the ground (4 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²),
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We need to rearrange this formula to solve for [tex]\( h \)[/tex]. Here's how you can do it step-by-step:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides of the equation to eliminate 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]
4. Substitute the known values into the equation:
- [tex]\( v = 4 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{4^2}{2 \times 32} \][/tex]
5. Calculate the value:
- [tex]\( 4^2 = 16 \)[/tex]
- [tex]\( 2 \times 32 = 64 \)[/tex]
- [tex]\( \frac{16}{64} = 0.25 \)[/tex]
The height ([tex]\( h \)[/tex]) from which the hammer was dropped is 0.25 feet above the ground.
Therefore, the correct answer is C. 0.25 feet.
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