Answer :
Sure! Let's solve the question step by step:
We need to find out how high above the ground the hammer was when it was dropped. We are given that the hammer hits the floor at a speed of 8 feet per second and the acceleration due to gravity is 32 feet per second squared. We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here:
- [tex]\( v \)[/tex] is the speed of the hammer when it hits the floor, which is 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We start by solving the formula for [tex]\( h \)[/tex]:
1. Square both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 2 \times 32 \times h \][/tex]
4. Simplify the equation:
[tex]\[ 64 = 64h \][/tex]
5. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
6. Simplify the expression:
[tex]\[ h = 1 \][/tex]
So, the hammer was dropped from a height of 1 foot above the ground. The correct answer is B. 1.0 foot.
We need to find out how high above the ground the hammer was when it was dropped. We are given that the hammer hits the floor at a speed of 8 feet per second and the acceleration due to gravity is 32 feet per second squared. We can use the formula:
[tex]\[ v = \sqrt{2gh} \][/tex]
Here:
- [tex]\( v \)[/tex] is the speed of the hammer when it hits the floor, which is 8 feet per second.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 32 feet per second squared.
- [tex]\( h \)[/tex] is the height from which the hammer was dropped.
We start by solving the formula for [tex]\( h \)[/tex]:
1. Square both sides of the equation to get rid of the square root:
[tex]\[ v^2 = 2gh \][/tex]
2. Plug in the values for [tex]\( v \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ 8^2 = 2 \times 32 \times h \][/tex]
3. Calculate [tex]\( 8^2 \)[/tex]:
[tex]\[ 64 = 2 \times 32 \times h \][/tex]
4. Simplify the equation:
[tex]\[ 64 = 64h \][/tex]
5. Solve for [tex]\( h \)[/tex] by dividing both sides by 64:
[tex]\[ h = \frac{64}{64} \][/tex]
6. Simplify the expression:
[tex]\[ h = 1 \][/tex]
So, the hammer was dropped from a height of 1 foot above the ground. The correct answer is B. 1.0 foot.
