Answer :
To find how far above the ground the hammer was when it was dropped, we can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity of the hammer, 4 feet per second in this case.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
- [tex]\( h \)[/tex] is the height above the ground that we need to find.
Let's solve for [tex]\( h \)[/tex] step-by-step:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Rearrange the equation to solve for [tex]\( h \)[/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 [tex]\( h \)[/tex]:
[tex]\[ h = \frac{16}{64} = 0.25 \][/tex]
Therefore, the hammer was dropped from a height of 0.25 feet above the ground. The correct answer is B. 0.25 feet.
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity of the hammer, 4 feet per second in this case.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
- [tex]\( h \)[/tex] is the height above the ground that we need to find.
Let's solve for [tex]\( h \)[/tex] step-by-step:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Rearrange the equation to solve for [tex]\( h \)[/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 [tex]\( h \)[/tex]:
[tex]\[ h = \frac{16}{64} = 0.25 \][/tex]
Therefore, the hammer was dropped from a height of 0.25 feet above the ground. The correct answer is B. 0.25 feet.
