Answer :
To determine how far above the ground the hammer was when you dropped it, we can use the formula provided:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the speed at which the hammer hits the floor, given as 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, given as 32 feet per second squared.
- [tex]\( h \)[/tex] is the height above the ground from which the hammer was dropped, which we need to find.
We can rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Start by squaring both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
3. Substitute the given values into this equation:
- [tex]\( v = 8 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet per second squared
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
4. Calculate [tex]\( 8^2 = 64 \)[/tex].
5. Multiply [tex]\( 2 \times 32 = 64 \)[/tex].
6. Finally, divide [tex]\( 64 \)[/tex] by [tex]\( 64 \)[/tex] to find [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was dropped from a height of 1.0 foot above the ground. The correct answer is A. 1.0 foot.
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the speed at which the hammer hits the floor, given as 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, given as 32 feet per second squared.
- [tex]\( h \)[/tex] is the height above the ground from which the hammer was dropped, which we need to find.
We can rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Start by squaring both sides to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
3. Substitute the given values into this equation:
- [tex]\( v = 8 \)[/tex] feet per second
- [tex]\( g = 32 \)[/tex] feet per second squared
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
4. Calculate [tex]\( 8^2 = 64 \)[/tex].
5. Multiply [tex]\( 2 \times 32 = 64 \)[/tex].
6. Finally, divide [tex]\( 64 \)[/tex] by [tex]\( 64 \)[/tex] to find [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
Therefore, the hammer was dropped from a height of 1.0 foot above the ground. The correct answer is A. 1.0 foot.
