Answer :
To solve the problem of finding how far above the ground the hammer was when you dropped it, we will use the given formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the hammer when it hits the floor, which is 8 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 above the ground we need to find.
We first rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ v = \sqrt{2gh} \][/tex]
Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
Now solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Substitute the known values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
First, calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Then multiply [tex]\( 2 \times 32 \)[/tex]:
[tex]\[ 2 \times 32 = 64 \][/tex]
Now divide the value of [tex]\( 8^2 \)[/tex] by [tex]\( 64 \)[/tex]:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was 1.0 foot above the ground when it was dropped. Hence, 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 floor, which is 8 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 above the ground we need to find.
We first rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ v = \sqrt{2gh} \][/tex]
Square both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
Now solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Substitute the known values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
First, calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Then multiply [tex]\( 2 \times 32 \)[/tex]:
[tex]\[ 2 \times 32 = 64 \][/tex]
Now divide the value of [tex]\( 8^2 \)[/tex] by [tex]\( 64 \)[/tex]:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was 1.0 foot above the ground when it was dropped. Hence, the correct answer is:
D. 1.0 foot
