Answer :
Sure! Let's solve the problem step-by-step using the given formula:
We are given:
- The final speed [tex]\( v \)[/tex] of the hammer when it hits the floor is 8 feet per second.
- The acceleration due to gravity [tex]\( g \)[/tex] is 32 feet/second².
We need to find the height [tex]\( h \)[/tex] from which the hammer was dropped. The formula we are using is:
[tex]\[ v = \sqrt{2gh} \][/tex]
The goal is to solve for [tex]\( h \)[/tex]. We'll start by squaring both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
Next, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, substitute the known values into the equation:
- [tex]\( v = 8 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Then, calculate:
[tex]\[ 2 \times 32 = 64 \][/tex]
Finally, divide:
[tex]\[ h = \frac{64}{64} = 1 \][/tex]
So, the height [tex]\( h \)[/tex] from which the hammer was dropped is 1.0 foot.
The correct option is:
A. 1.0 foot
We are given:
- The final speed [tex]\( v \)[/tex] of the hammer when it hits the floor is 8 feet per second.
- The acceleration due to gravity [tex]\( g \)[/tex] is 32 feet/second².
We need to find the height [tex]\( h \)[/tex] from which the hammer was dropped. The formula we are using is:
[tex]\[ v = \sqrt{2gh} \][/tex]
The goal is to solve for [tex]\( h \)[/tex]. We'll start by squaring both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
Next, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Now, substitute the known values into the equation:
- [tex]\( v = 8 \)[/tex] feet/second
- [tex]\( g = 32 \)[/tex] feet/second²
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Then, calculate:
[tex]\[ 2 \times 32 = 64 \][/tex]
Finally, divide:
[tex]\[ h = \frac{64}{64} = 1 \][/tex]
So, the height [tex]\( h \)[/tex] from which the hammer was dropped is 1.0 foot.
The correct option is:
A. 1.0 foot
