Answer :
Let's solve the problem of finding how far above the ground the hammer was when it was dropped, step by step.
We have the formula for the speed of a falling object:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity (speed) of the hammer when it hits the ground, which is given as 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is given as 32 feet per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped, and this is what we need to find.
To find the height [tex]\( h \)[/tex], we will rearrange the formula. First, square both sides to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
Next, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, substitute the given values into the equation:
- [tex]\( v = 12 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet per second squared
Calculate:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
Therefore, the height [tex]\( h \)[/tex] from which the hammer was dropped is 2.25 feet.
The correct answer is D. 2.25 feet.
We have the formula for the speed of a falling object:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity (speed) of the hammer when it hits the ground, which is given as 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is given as 32 feet per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped, and this is what we need to find.
To find the height [tex]\( h \)[/tex], we will rearrange the formula. First, square both sides to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
Next, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, substitute the given values into the equation:
- [tex]\( v = 12 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet per second squared
Calculate:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
Therefore, the height [tex]\( h \)[/tex] from which the hammer was dropped is 2.25 feet.
The correct answer is D. 2.25 feet.
