Answer :
To solve this problem, we'll use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where [tex]\( v \)[/tex] is the velocity when the hammer hits the floor, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We are given:
- [tex]\( v = 4 \)[/tex] feet per second (the speed when the hammer hits the floor)
- [tex]\( g = 32 \)[/tex] feet per second squared (the acceleration due to gravity)
We need to find [tex]\( h \)[/tex], the height.
1. Start by squaring both sides of the formula to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the known values [tex]\( v = 4 \)[/tex] and [tex]\( g = 32 \)[/tex] into the equation:
[tex]\[ 4^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 4^2 \)[/tex] to get 16:
[tex]\[ 16 = 2 \times 32 \times h \][/tex]
4. Multiply 2 and 32 to get 64:
[tex]\[ 16 = 64 \times h \][/tex]
5. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{16}{64} \][/tex]
6. Simplify [tex]\(\frac{16}{64}\)[/tex] to [tex]\(\frac{1}{4}\)[/tex], which is 0.25.
Therefore, the height [tex]\( h \)[/tex] from which the hammer was dropped is 0.25 feet.
The correct answer is C. 0.25 feet.
[tex]\[ v = \sqrt{2gh} \][/tex]
where [tex]\( v \)[/tex] is the velocity when the hammer hits the floor, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We are given:
- [tex]\( v = 4 \)[/tex] feet per second (the speed when the hammer hits the floor)
- [tex]\( g = 32 \)[/tex] feet per second squared (the acceleration due to gravity)
We need to find [tex]\( h \)[/tex], the height.
1. Start by squaring both sides of the formula to remove the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the known values [tex]\( v = 4 \)[/tex] and [tex]\( g = 32 \)[/tex] into the equation:
[tex]\[ 4^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 4^2 \)[/tex] to get 16:
[tex]\[ 16 = 2 \times 32 \times h \][/tex]
4. Multiply 2 and 32 to get 64:
[tex]\[ 16 = 64 \times h \][/tex]
5. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{16}{64} \][/tex]
6. Simplify [tex]\(\frac{16}{64}\)[/tex] to [tex]\(\frac{1}{4}\)[/tex], which is 0.25.
Therefore, the height [tex]\( h \)[/tex] from which the hammer was dropped is 0.25 feet.
The correct answer is C. 0.25 feet.
