Answer :
To find out how far above the ground the hammer was when you dropped it, we can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed at which the hammer 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.
Let's solve the formula for [tex]\( h \)[/tex]:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Substitute the given values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
So, the height [tex]\( h \)[/tex] from which the hammer was dropped is 1.0 foot.
Thus, the correct option is C. 1.0 foot.
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed at which the hammer 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.
Let's solve the formula for [tex]\( h \)[/tex]:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Substitute the given values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate:
[tex]\[ h = \frac{64}{64} = 1.0 \][/tex]
So, the height [tex]\( h \)[/tex] from which the hammer was dropped is 1.0 foot.
Thus, the correct option is C. 1.0 foot.
