Answer :
To solve this problem, we need to find the height [tex]\( h \)[/tex] from which the hammer was dropped. We're given that the speed [tex]\( v \)[/tex] of the hammer when it hits the ground is 8 feet per second, and the acceleration due to gravity [tex]\( g \)[/tex] is 32 feet/second². We'll use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here's how we can find [tex]\( h \)[/tex]:
1. Square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the given values into the equation. We know [tex]\( v = 8 \)[/tex] and [tex]\( g = 32 \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
[tex]\[ 64 = 64h \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1 \][/tex]
Therefore, the height [tex]\( h \)[/tex] from which the hammer was dropped is 1.0 foot. This matches option C in the provided choices.
[tex]\[ v = \sqrt{2gh} \][/tex]
Here's how we can find [tex]\( h \)[/tex]:
1. Square both sides of the equation to eliminate the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Substitute the given values into the equation. We know [tex]\( v = 8 \)[/tex] and [tex]\( g = 32 \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
[tex]\[ 64 = 64h \][/tex]
3. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1 \][/tex]
Therefore, the height [tex]\( h \)[/tex] from which the hammer was dropped is 1.0 foot. This matches option C in the provided choices.
