Answer :
To find how far above the ground the hammer was when it was dropped, we can use the provided formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
In this formula:
- [tex]\( v \)[/tex] is the final velocity of the hammer when it hits the floor, which is given as 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
We need to find [tex]\( h \)[/tex], the height from which the hammer was dropped.
1. Start with the formula and substitute the known values:
[tex]\[ 8 = \sqrt{2 \times 32 \times h} \][/tex]
2. To remove the square root, square both sides:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 2 \times 32 \times h \][/tex]
4. Calculate [tex]\( 2 \times 32 \)[/tex]:
[tex]\[ 64 = 64 \times h \][/tex]
5. Divide both sides by 64 to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} \][/tex]
6. This simplifies to:
[tex]\[ h = 1 \][/tex]
Therefore, the hammer was dropped from a height of 1 foot above the ground.
[tex]\[ v = \sqrt{2gh} \][/tex]
In this formula:
- [tex]\( v \)[/tex] is the final velocity of the hammer when it hits the floor, which is given as 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
We need to find [tex]\( h \)[/tex], the height from which the hammer was dropped.
1. Start with the formula and substitute the known values:
[tex]\[ 8 = \sqrt{2 \times 32 \times h} \][/tex]
2. To remove the square root, square both sides:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 2 \times 32 \times h \][/tex]
4. Calculate [tex]\( 2 \times 32 \)[/tex]:
[tex]\[ 64 = 64 \times h \][/tex]
5. Divide both sides by 64 to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{64}{64} \][/tex]
6. This simplifies to:
[tex]\[ h = 1 \][/tex]
Therefore, the hammer was dropped from a height of 1 foot above the ground.
