Answer :
To solve the problem of determining the height from which the hammer was dropped, we use the formula for velocity when an object is dropped from a certain height:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the velocity with which the hammer hits the ground (12 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.
We want to solve for [tex]\( h \)[/tex]. Let's rearrange the formula to make [tex]\( h \)[/tex] the subject:
1. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, plug in the given values:
- [tex]\( v = 12 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
Substitute these values into the equation:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} \][/tex]
[tex]\[ h = 2.25 \][/tex] feet
Thus, the height from which the hammer was dropped is 2.25 feet. Therefore, the correct answer is:
B. 2.25 feet
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the velocity with which the hammer hits the ground (12 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.
We want to solve for [tex]\( h \)[/tex]. Let's rearrange the formula to make [tex]\( h \)[/tex] the subject:
1. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, plug in the given values:
- [tex]\( v = 12 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
Substitute these values into the equation:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} \][/tex]
[tex]\[ h = 2.25 \][/tex] feet
Thus, the height from which the hammer was dropped is 2.25 feet. Therefore, the correct answer is:
B. 2.25 feet
