Answer :
To find out how far above the ground the hammer was when it was dropped, we will use the formula given:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity of the hammer when it hits the floor, which is 4 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height above the ground from which the hammer was dropped.
Our goal is to solve for [tex]\( h \)[/tex]. Let's go through the steps:
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. Substitute the given values into the equation. We have [tex]\( v = 4 \)[/tex] and [tex]\( g = 32 \)[/tex]:
[tex]\[ 4^2 = 2 \times 32 \times h \][/tex]
4. Calculate [tex]\( 4^2 \)[/tex] which is 16:
[tex]\[ 16 = 64h \][/tex]
5. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{16}{64} \][/tex]
6. Simplify the fraction:
[tex]\[ h = 0.25 \][/tex]
So, the hammer was dropped from a height of 0.25 feet above the ground. Therefore, the correct answer is option C: 0.25 feet.
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity of the hammer when it hits the floor, which is 4 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height above the ground from which the hammer was dropped.
Our goal is to solve for [tex]\( h \)[/tex]. Let's go through the steps:
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. Substitute the given values into the equation. We have [tex]\( v = 4 \)[/tex] and [tex]\( g = 32 \)[/tex]:
[tex]\[ 4^2 = 2 \times 32 \times h \][/tex]
4. Calculate [tex]\( 4^2 \)[/tex] which is 16:
[tex]\[ 16 = 64h \][/tex]
5. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{16}{64} \][/tex]
6. Simplify the fraction:
[tex]\[ h = 0.25 \][/tex]
So, the hammer was dropped from a height of 0.25 feet above the ground. Therefore, the correct answer is option C: 0.25 feet.
