Answer :
To solve this problem, we need to find the height from which a hammer was dropped, given that it hits the floor at a speed of 12 feet per second. The acceleration due to gravity is 32 feet per second squared.
We will use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed (12 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet per second squared),
- [tex]\( h \)[/tex] is the height above the ground.
Here's a step-by-step solution:
1. Square the speed:
Start by squaring the speed ([tex]\( v \)[/tex]).
[tex]\[ v^2 = 12^2 = 144 \][/tex]
2. Set up the equation:
Substitute [tex]\( v^2 \)[/tex] and [tex]\( g \)[/tex] into the equation:
[tex]\[ 144 = 2 \times 32 \times h \][/tex]
3. Solve for [tex]\( h \)[/tex]:
Rearrange the equation to isolate [tex]\( h \)[/tex] on one side:
[tex]\[ h = \frac{144}{2 \times 32} \][/tex]
4. Calculate the height:
Simplify the equation:
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
Thus, the height from which the hammer was dropped is 2.25 feet.
Therefore, the correct answer is: C. 2.25 feet.
We will use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed (12 feet per second),
- [tex]\( g \)[/tex] is the acceleration due to gravity (32 feet per second squared),
- [tex]\( h \)[/tex] is the height above the ground.
Here's a step-by-step solution:
1. Square the speed:
Start by squaring the speed ([tex]\( v \)[/tex]).
[tex]\[ v^2 = 12^2 = 144 \][/tex]
2. Set up the equation:
Substitute [tex]\( v^2 \)[/tex] and [tex]\( g \)[/tex] into the equation:
[tex]\[ 144 = 2 \times 32 \times h \][/tex]
3. Solve for [tex]\( h \)[/tex]:
Rearrange the equation to isolate [tex]\( h \)[/tex] on one side:
[tex]\[ h = \frac{144}{2 \times 32} \][/tex]
4. Calculate the height:
Simplify the equation:
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
Thus, the height from which the hammer was dropped is 2.25 feet.
Therefore, the correct answer is: C. 2.25 feet.
