Answer :
To find the height from which the hammer was dropped, we can use the formula for the velocity of an object falling freely under gravity:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity 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 per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped, and this is what we want to find.
Let's solve for [tex]\( h \)[/tex]:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Rearrange the equation to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Substitute the known values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate [tex]\( 8^2 \)[/tex], which is 64. Then multiply 2 by 32, which is 64.
6. Divide 64 by 64 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. So, the correct answer is:
B. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity 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 per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped, and this is what we want to find.
Let's solve for [tex]\( h \)[/tex]:
1. Start with the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Rearrange the equation to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Substitute the known values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
5. Calculate [tex]\( 8^2 \)[/tex], which is 64. Then multiply 2 by 32, which is 64.
6. Divide 64 by 64 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. So, the correct answer is:
B. 1.0 foot
