Answer :
To find out how high above the ground the hammer was when it was dropped, you can use the formula for the velocity of an object in free fall:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here, [tex]\( v \)[/tex] represents the velocity of the object when it hits the ground, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height from which the object was dropped.
Given values:
- [tex]\( v = 4 \)[/tex] feet per second (the speed at which the hammer hits the floor),
- [tex]\( g = 32 \)[/tex] feet per second squared (the acceleration due to gravity).
We need to rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Start with the original formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Substitute the known values into the equation:
[tex]\[ h = \frac{4^2}{2 \times 32} \][/tex]
5. Calculate the result:
[tex]\[ h = \frac{16}{64} = 0.25 \][/tex]
Therefore, the hammer was dropped from a height of 0.25 feet above the ground. So the correct answer is:
D. 0.25 feet
[tex]\[ v = \sqrt{2gh} \][/tex]
Here, [tex]\( v \)[/tex] represents the velocity of the object when it hits the ground, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height from which the object was dropped.
Given values:
- [tex]\( v = 4 \)[/tex] feet per second (the speed at which the hammer hits the floor),
- [tex]\( g = 32 \)[/tex] feet per second squared (the acceleration due to gravity).
We need to rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Start with the original formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
2. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
4. Substitute the known values into the equation:
[tex]\[ h = \frac{4^2}{2 \times 32} \][/tex]
5. Calculate the result:
[tex]\[ h = \frac{16}{64} = 0.25 \][/tex]
Therefore, the hammer was dropped from a height of 0.25 feet above the ground. So the correct answer is:
D. 0.25 feet
