Answer :
To solve this problem, we need to find out how high above the ground the hammer was when you dropped it. We're given the speed at which the hammer hits the floor (4 feet per second) and the acceleration due to gravity (32 feet/second²).
We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed (4 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²),
- [tex]\( h \)[/tex] is the height we need to find.
First, we'll rearrange the formula to solve for [tex]\( h \)[/tex]:
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 known values:
- [tex]\( v = 4 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second²
Substitute these into the formula:
[tex]\[ h = \frac{4^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{16}{64} \][/tex]
[tex]\[ h = 0.25 \][/tex] feet
So the height from which the hammer was dropped is 0.25 feet. Therefore, the correct answer is option C: 0.25 feet.
We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed (4 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet/second²),
- [tex]\( h \)[/tex] is the height we need to find.
First, we'll rearrange the formula to solve for [tex]\( h \)[/tex]:
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 known values:
- [tex]\( v = 4 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet/second²
Substitute these into the formula:
[tex]\[ h = \frac{4^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{16}{64} \][/tex]
[tex]\[ h = 0.25 \][/tex] feet
So the height from which the hammer was dropped is 0.25 feet. Therefore, the correct answer is option C: 0.25 feet.
