Answer :
To solve this problem, we need to determine the height from which the hammer was dropped using the given formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity of the hammer when it hit the ground, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
Our goal is to find [tex]\( h \)[/tex], the height from which the hammer was dropped.
1. Start by squaring both sides of the formula to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the known values into the equation:
[tex]\[ 12^2 = 2 \times 32 \times h \][/tex]
3. Compute [tex]\( 12^2 \)[/tex], which is 144:
[tex]\[ 144 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides of the equation by 64:
[tex]\[ h = \frac{144}{64} \][/tex]
5. Simplify the fraction:
[tex]\[ h = 2.25 \][/tex]
Therefore, the hammer was dropped from a height of 2.25 feet above the ground. Thus, the correct answer is:
A. 2.25 feet
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity of the hammer when it hit the ground, which is 12 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet/second².
Our goal is to find [tex]\( h \)[/tex], the height from which the hammer was dropped.
1. Start by squaring both sides of the formula to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the known values into the equation:
[tex]\[ 12^2 = 2 \times 32 \times h \][/tex]
3. Compute [tex]\( 12^2 \)[/tex], which is 144:
[tex]\[ 144 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides of the equation by 64:
[tex]\[ h = \frac{144}{64} \][/tex]
5. Simplify the fraction:
[tex]\[ h = 2.25 \][/tex]
Therefore, the hammer was dropped from a height of 2.25 feet above the ground. Thus, the correct answer is:
A. 2.25 feet
