Convert mach to yard / second
Learn how to convert
1
mach to
yard / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(mach\right)={\color{rgb(20,165,174)} x}\left(\dfrac{yard}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(mach\right) = {\color{rgb(89,182,91)} 331.0\left(\dfrac{meter}{second}\right)} = {\color{rgb(89,182,91)} 331.0\left(\dfrac{m}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{yard}{second}\right) = {\color{rgb(125,164,120)} 0.9144\left(\dfrac{meter}{second}\right)} = {\color{rgb(125,164,120)} 0.9144\left(\dfrac{m}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(mach\right)={\color{rgb(20,165,174)} x}\left(\dfrac{yard}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 331.0} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 0.9144}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 331.0} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 0.9144} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 331.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 0.9144} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(331.0 = {\color{rgb(20,165,174)} x} \times 0.9144\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 0.9144 = 331.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{0.9144}\right)\)
\({\color{rgb(20,165,174)} x} \times 0.9144 \times \dfrac{1.0}{0.9144} = 331.0 \times \dfrac{1.0}{0.9144}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{0.9144}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{0.9144}}} = 331.0 \times \dfrac{1.0}{0.9144}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{331.0}{0.9144}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx361.98600175\approx3.6199 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(mach\right)\approx{\color{rgb(20,165,174)} 3.6199 \times 10^{2}}\left(\dfrac{yard}{second}\right)\)