Answer :
Let's solve this problem step by step using the formula provided:
1. Understand the Formula: We are given the formula for speed of the hammer as it hits the floor:
[tex]\[
v = \sqrt{2gh}
\][/tex]
where [tex]\( v \)[/tex] is the speed, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height from which the hammer was dropped.
2. Substitute Known Values:
- The speed [tex]\( v \)[/tex] is 4 feet per second.
- The acceleration due to gravity [tex]\( g \)[/tex] is 32 feet per second squared.
3. Rearrange the Formula to Solve for [tex]\( h \)[/tex]:
[tex]\[
v^2 = 2gh
\][/tex]
[tex]\[
h = \frac{v^2}{2g}
\][/tex]
4. Calculate [tex]\( h \)[/tex]:
- First, calculate the square of the speed: [tex]\( v^2 = 4^2 = 16 \)[/tex].
- Substitute [tex]\( v^2 = 16 \)[/tex] and [tex]\( g = 32 \)[/tex] into the equation:
[tex]\[
h = \frac{16}{2 \times 32} = \frac{16}{64} = 0.25
\][/tex]
Therefore, the hammer was dropped from a height of 0.25 feet above the ground. The correct answer is option B, 0.25 feet.
1. Understand the Formula: We are given the formula for speed of the hammer as it hits the floor:
[tex]\[
v = \sqrt{2gh}
\][/tex]
where [tex]\( v \)[/tex] is the speed, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height from which the hammer was dropped.
2. Substitute Known Values:
- The speed [tex]\( v \)[/tex] is 4 feet per second.
- The acceleration due to gravity [tex]\( g \)[/tex] is 32 feet per second squared.
3. Rearrange the Formula to Solve for [tex]\( h \)[/tex]:
[tex]\[
v^2 = 2gh
\][/tex]
[tex]\[
h = \frac{v^2}{2g}
\][/tex]
4. Calculate [tex]\( h \)[/tex]:
- First, calculate the square of the speed: [tex]\( v^2 = 4^2 = 16 \)[/tex].
- Substitute [tex]\( v^2 = 16 \)[/tex] and [tex]\( g = 32 \)[/tex] into the equation:
[tex]\[
h = \frac{16}{2 \times 32} = \frac{16}{64} = 0.25
\][/tex]
Therefore, the hammer was dropped from a height of 0.25 feet above the ground. The correct answer is option B, 0.25 feet.
