We appreciate your visit to While working on a roof Rob dropped his hammer The hammer s fall can be represented by the equation tex h 16t 2 20 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find out how long it will take for the hammer to reach the ground, we need to determine when the height [tex]\( h \)[/tex] becomes 0. This involves solving the equation for [tex]\( h \)[/tex]:
[tex]\[
h = -16t^2 + 20
\][/tex]
1. Set the equation equal to zero, since the hammer reaches the ground at [tex]\( h = 0 \)[/tex]:
[tex]\[
0 = -16t^2 + 20
\][/tex]
2. Rearrange the equation to solve for [tex]\( t^2 \)[/tex]:
[tex]\[
16t^2 = 20
\][/tex]
3. Divide both sides by 16 to isolate [tex]\( t^2 \)[/tex]:
[tex]\[
t^2 = \frac{20}{16}
\][/tex]
4. Simplify the fraction:
[tex]\[
t^2 = 1.25
\][/tex]
5. Take the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[
t = \sqrt{1.25}
\][/tex]
6. Calculate the square root to find the time [tex]\( t \)[/tex]:
[tex]\[
t \approx 1.118
\][/tex]
Thus, it will take approximately 1.118 seconds for the hammer to reach the ground.
[tex]\[
h = -16t^2 + 20
\][/tex]
1. Set the equation equal to zero, since the hammer reaches the ground at [tex]\( h = 0 \)[/tex]:
[tex]\[
0 = -16t^2 + 20
\][/tex]
2. Rearrange the equation to solve for [tex]\( t^2 \)[/tex]:
[tex]\[
16t^2 = 20
\][/tex]
3. Divide both sides by 16 to isolate [tex]\( t^2 \)[/tex]:
[tex]\[
t^2 = \frac{20}{16}
\][/tex]
4. Simplify the fraction:
[tex]\[
t^2 = 1.25
\][/tex]
5. Take the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[
t = \sqrt{1.25}
\][/tex]
6. Calculate the square root to find the time [tex]\( t \)[/tex]:
[tex]\[
t \approx 1.118
\][/tex]
Thus, it will take approximately 1.118 seconds for the hammer to reach the ground.
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