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Answer :
To find how far above the ground the hammer was when you dropped it, we can use the formula for velocity in terms of gravity and height:
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity when the hammer hits the ground,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We are given:
- The velocity [tex]\( v = 8 \)[/tex] feet per second,
- The acceleration due to gravity [tex]\( g = 32 \)[/tex] feet/second².
We need to solve for [tex]\( h \)[/tex]. First, we'll rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Square both sides of the equation to get rid of 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]
Substitute the given values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \, \text{foot} \][/tex]
Therefore, the hammer was 1.0 foot above the ground when it was dropped. Thus, the correct answer is B. 1.0 foot.
[tex]\[ v = \sqrt{2gh} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity when the hammer hits the ground,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We are given:
- The velocity [tex]\( v = 8 \)[/tex] feet per second,
- The acceleration due to gravity [tex]\( g = 32 \)[/tex] feet/second².
We need to solve for [tex]\( h \)[/tex]. First, we'll rearrange the formula to solve for [tex]\( h \)[/tex]:
1. Square both sides of the equation to get rid of 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]
Substitute the given values into the equation:
[tex]\[ h = \frac{8^2}{2 \times 32} \][/tex]
[tex]\[ h = \frac{64}{64} \][/tex]
[tex]\[ h = 1.0 \, \text{foot} \][/tex]
Therefore, the hammer was 1.0 foot above the ground when it was dropped. Thus, the correct answer is B. 1.0 foot.
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