Answer :
To find out how far above the ground the hammer was when it was dropped, we can use the formula for velocity due to gravity:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity of the hammer when it hits the ground, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped, which we need to find.
First, we'll solve the equation for [tex]\( h \)[/tex]:
1. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the given values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 12^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 12^2 \)[/tex]:
[tex]\[ 144 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{144}{64} \][/tex]
5. Simplify the fraction:
[tex]\[ h = 2.25 \][/tex]
Thus, the hammer was dropped from a height of 2.25 feet. The correct answer is B. 2.25 feet.
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity of the hammer when it hits the ground, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped, which we need to find.
First, we'll solve the equation for [tex]\( h \)[/tex]:
1. Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the given values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 12^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 12^2 \)[/tex]:
[tex]\[ 144 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{144}{64} \][/tex]
5. Simplify the fraction:
[tex]\[ h = 2.25 \][/tex]
Thus, the hammer was dropped from a height of 2.25 feet. The correct answer is B. 2.25 feet.
