Answer :
To solve this problem, we use the formula for the final velocity of a falling object:
[tex]\[ v = \sqrt{2 \cdot g \cdot h} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity when the object hits the ground.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared (given).
- [tex]\( h \)[/tex] is the height from which the object was initially dropped.
We are given that the velocity [tex]\( v \)[/tex] is 12 feet per second when the hammer hits the ground.
Our goal is to find [tex]\( h \)[/tex].
1. First, square both sides of the formula to eliminate the square root:
[tex]\[ v^2 = 2 \cdot g \cdot h \][/tex]
2. Next, isolate [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2 \cdot g \)[/tex]:
[tex]\[ h = \frac{v^2}{2 \cdot g} \][/tex]
3. Substitute the known values into the formula:
- [tex]\( v = 12 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet per second squared
[tex]\[ h = \frac{12^2}{2 \cdot 32} \][/tex]
4. Calculate [tex]\( 12^2 \)[/tex], which is 144.
5. Multiply [tex]\( 2 \cdot 32 \)[/tex] to get 64.
6. Finally, divide 144 by 64 to find [tex]\( h \)[/tex]:
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
Thus, the hammer was dropped from a height of 2.25 feet. Therefore, the correct answer is:
C. 2.25 feet
[tex]\[ v = \sqrt{2 \cdot g \cdot h} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity when the object hits the ground.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared (given).
- [tex]\( h \)[/tex] is the height from which the object was initially dropped.
We are given that the velocity [tex]\( v \)[/tex] is 12 feet per second when the hammer hits the ground.
Our goal is to find [tex]\( h \)[/tex].
1. First, square both sides of the formula to eliminate the square root:
[tex]\[ v^2 = 2 \cdot g \cdot h \][/tex]
2. Next, isolate [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2 \cdot g \)[/tex]:
[tex]\[ h = \frac{v^2}{2 \cdot g} \][/tex]
3. Substitute the known values into the formula:
- [tex]\( v = 12 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet per second squared
[tex]\[ h = \frac{12^2}{2 \cdot 32} \][/tex]
4. Calculate [tex]\( 12^2 \)[/tex], which is 144.
5. Multiply [tex]\( 2 \cdot 32 \)[/tex] to get 64.
6. Finally, divide 144 by 64 to find [tex]\( h \)[/tex]:
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
Thus, the hammer was dropped from a height of 2.25 feet. Therefore, the correct answer is:
C. 2.25 feet
