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Answer :
To solve this problem, we need to find the height from which the hammer was dropped. We are given that its speed upon hitting the floor is 12 feet per second, and the acceleration due to gravity is 32 feet per second squared. We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here:
- [tex]\( v \)[/tex] is the speed when the hammer hits the floor, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height above the ground we want to find.
To find [tex]\( h \)[/tex], we can rearrange the formula as follows:
1. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, plug in the values we know:
- [tex]\( v = 12 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
Calculate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} \][/tex]
[tex]\[ h = 2.25 \text{ feet} \][/tex]
Therefore, the hammer was dropped from a height of 2.25 feet above the ground. The correct answer is A. 2.25 feet.
[tex]\[ v = \sqrt{2gh} \][/tex]
Here:
- [tex]\( v \)[/tex] is the speed when the hammer hits the floor, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height above the ground we want to find.
To find [tex]\( h \)[/tex], we can rearrange the formula as follows:
1. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, plug in the values we know:
- [tex]\( v = 12 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
Calculate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} \][/tex]
[tex]\[ h = 2.25 \text{ feet} \][/tex]
Therefore, the hammer was dropped from a height of 2.25 feet above the ground. The correct answer is A. 2.25 feet.
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