Answer :
To find out how high above the ground the hammer was when you dropped it, we can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the speed of the hammer when it hits the floor, 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.
First, we need to solve for [tex]\( h \)[/tex]. We can rearrange the formula to:
[tex]\[ v^2 = 2gh \][/tex]
Now, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Substitute the known values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
Calculate the square of the speed:
[tex]\[ 8^2 = 64 \][/tex]
Now substitute that into the equation:
[tex]\[ h = \frac{64}{2 \times 32} \][/tex]
Calculate the denominator:
[tex]\[ 2 \times 32 = 64 \][/tex]
Now divide the numerator by the denominator:
[tex]\[ h = \frac{64}{64} = 1 \][/tex]
So, the hammer was dropped from a height of 1.0 foot.
The correct answer is:
A. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the speed of the hammer when it hits the floor, 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.
First, we need to solve for [tex]\( h \)[/tex]. We can rearrange the formula to:
[tex]\[ v^2 = 2gh \][/tex]
Now, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Substitute the known values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
Calculate the square of the speed:
[tex]\[ 8^2 = 64 \][/tex]
Now substitute that into the equation:
[tex]\[ h = \frac{64}{2 \times 32} \][/tex]
Calculate the denominator:
[tex]\[ 2 \times 32 = 64 \][/tex]
Now divide the numerator by the denominator:
[tex]\[ h = \frac{64}{64} = 1 \][/tex]
So, the hammer was dropped from a height of 1.0 foot.
The correct answer is:
A. 1.0 foot
