Answer :
Certainly! Let's solve the problem step-by-step using the given formula:
The formula you need is:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed when the hammer hits the floor, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We need to solve for [tex]\( h \)[/tex]. Start by rearranging the formula to solve for [tex]\( h \)[/tex]:
1. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Insert the known values into the equation:
- [tex]\( v = 12 \)[/tex]
- [tex]\( g = 32 \)[/tex]
Now substitute those values into the equation:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} \][/tex]
When you simplify the fraction:
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
So, the hammer was dropped from a height of 2.25 feet. Therefore, the correct answer is:
A. 2.25 feet
The formula you need is:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed when the hammer hits the floor, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We need to solve for [tex]\( h \)[/tex]. Start by rearranging the formula to solve for [tex]\( h \)[/tex]:
1. Square both sides to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( 2g \)[/tex]:
[tex]\[ h = \frac{v^2}{2g} \][/tex]
Insert the known values into the equation:
- [tex]\( v = 12 \)[/tex]
- [tex]\( g = 32 \)[/tex]
Now substitute those values into the equation:
[tex]\[ h = \frac{12^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{144}{64} \][/tex]
When you simplify the fraction:
[tex]\[ h = \frac{144}{64} = 2.25 \][/tex]
So, the hammer was dropped from a height of 2.25 feet. Therefore, the correct answer is:
A. 2.25 feet
