Answer :
To find out how far above the ground the hammer was when it was dropped, we can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity when the hammer 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 it is what we need to find.
Let's solve for [tex]\( h \)[/tex] using the formula:
1. Start by squaring both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the given values:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Simplify the left side of the equation:
[tex]\[ 64 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
5. So, [tex]\( h = 1.0 \)[/tex] foot.
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 final velocity when the hammer 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 it is what we need to find.
Let's solve for [tex]\( h \)[/tex] using the formula:
1. Start by squaring both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the given values:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Simplify the left side of the equation:
[tex]\[ 64 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
5. So, [tex]\( h = 1.0 \)[/tex] foot.
Therefore, the hammer was dropped from a height of 1.0 foot above the ground. The correct answer is A. 1.0 foot.
