Answer :
Let's solve the problem step-by-step!
We are given that the speed of the hammer when it hits the ground is 4 feet per second and the acceleration due to gravity is 32 feet per second squared. We need to find out how high above the ground the hammer was when it was dropped.
We'll use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity, 4 feet per second,
- [tex]\( g \)[/tex] is the acceleration due to gravity, 32 feet per second squared,
- [tex]\( h \)[/tex] is the height above the ground in feet.
To find [tex]\( h \)[/tex], we can rearrange the formula to solve for [tex]\( h \)[/tex] as follows:
1. Square both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the values we know:
[tex]\[ 4^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 4^2 \)[/tex]:
[tex]\[ 16 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{16}{64} \][/tex]
5. Simplify the fraction:
[tex]\[ h = 0.25 \][/tex]
Thus, the hammer was dropped from a height of [tex]\( 0.25 \)[/tex] feet above the ground. So, the correct answer is:
B. 0.25 feet
We are given that the speed of the hammer when it hits the ground is 4 feet per second and the acceleration due to gravity is 32 feet per second squared. We need to find out how high above the ground the hammer was when it was dropped.
We'll use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity, 4 feet per second,
- [tex]\( g \)[/tex] is the acceleration due to gravity, 32 feet per second squared,
- [tex]\( h \)[/tex] is the height above the ground in feet.
To find [tex]\( h \)[/tex], we can rearrange the formula to solve for [tex]\( h \)[/tex] as follows:
1. Square both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the values we know:
[tex]\[ 4^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 4^2 \)[/tex]:
[tex]\[ 16 = 64h \][/tex]
4. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{16}{64} \][/tex]
5. Simplify the fraction:
[tex]\[ h = 0.25 \][/tex]
Thus, the hammer was dropped from a height of [tex]\( 0.25 \)[/tex] feet above the ground. So, the correct answer is:
B. 0.25 feet
