Answer :
To determine how far above the ground the hammer was when you dropped it, you can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final 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 we want to find.
We need to solve for [tex]\( h \)[/tex]. Let's go through the steps:
1. Start by squaring both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} = 1 \][/tex]
Thus, the hammer was 1.0 foot above the ground when you dropped it.
The correct answer is:
C. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final 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 we want to find.
We need to solve for [tex]\( h \)[/tex]. Let's go through the steps:
1. Start by squaring both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} = 1 \][/tex]
Thus, the hammer was 1.0 foot above the ground when you dropped it.
The correct answer is:
C. 1.0 foot
