Answer :
To solve this problem, we need to find out how high the hammer was above the ground when it was dropped. We're given the formula for speed:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the hammer when it hits the ground, which is 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We need to rearrange this formula to solve for [tex]\( h \)[/tex]. Start by squaring both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
Now let's solve for [tex]\( h \)[/tex]:
1. Divide both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, plug in the given values:
- [tex]\( v = 8 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Now, calculate the denominator:
[tex]\[ 2 \times 32 = 64 \][/tex]
Using these calculations, find [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was 1.0 foot above the ground when it was dropped.
The correct answer is D. 1.0 foot.
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the hammer when it hits the ground, which is 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We need to rearrange this formula to solve for [tex]\( h \)[/tex]. Start by squaring both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
Now let's solve for [tex]\( h \)[/tex]:
1. Divide both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, plug in the given values:
- [tex]\( v = 8 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Now, calculate the denominator:
[tex]\[ 2 \times 32 = 64 \][/tex]
Using these calculations, find [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was 1.0 foot above the ground when it was dropped.
The correct answer is D. 1.0 foot.
