Answer :
To find out how far above the ground the hammer was when you dropped it, we can use the given formula for velocity:
[tex]\[ v = \sqrt{2gh} \][/tex]
We need to solve this equation for [tex]\( h \)[/tex]. Let's go through the steps:
1. First, square both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. We know the velocity ([tex]\( v \)[/tex]) when the hammer hits the ground is 8 feet per second, and the acceleration due to gravity ([tex]\( g \)[/tex]) is 32 feet per second squared. Substitute these values into the equation:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 64h \][/tex]
4. To find [tex]\( h \)[/tex], divide both sides of the equation by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
5. Simplify the right-hand side:
[tex]\[ h = 1 \][/tex]
Therefore, the hammer was 1.0 foot above the ground when you dropped it. So the correct answer is:
B. 1.0 foot
[tex]\[ v = \sqrt{2gh} \][/tex]
We need to solve this equation for [tex]\( h \)[/tex]. Let's go through the steps:
1. First, square both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. We know the velocity ([tex]\( v \)[/tex]) when the hammer hits the ground is 8 feet per second, and the acceleration due to gravity ([tex]\( g \)[/tex]) is 32 feet per second squared. Substitute these values into the equation:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 64h \][/tex]
4. To find [tex]\( h \)[/tex], divide both sides of the equation by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
5. Simplify the right-hand side:
[tex]\[ h = 1 \][/tex]
Therefore, the hammer was 1.0 foot above the ground when you dropped it. So the correct answer is:
B. 1.0 foot
