Question

An airplane traveling north at 220 m/s encounters a 50-m/s crosswind from west to east. What is its resultant velocity?

Answer 1

Answer:

We can calculate the resultant speed of the plane by using the Pythagorean Theorem since both speeds are perpendicular (forming a right triangle).

So, calculating we have:

\begin{gathered}ResultantSpeed=\sqrt{VerticalSpeed^{2}+HorizontalSpeed^{2}}\\\\ResultantSpeed=\sqrt{(220\frac{m}{s})^{2}+50\frac{m}{s})^{2}\end{gathered}

\begin{gathered}ResulntantSpeed=\sqrt{48400\frac{m^{2} }{s^{2} }+2500\frac{m^{2} }{s^{2} } } \\\\ResultantSpeed=\sqrt{50900\frac{m^{2} }{s^{2} }}=226\frac{m}{s}\end{gathered}

ResulntantSpeed=

48400

s

2

m

2

+2500

s

2

m

2

ResultantSpeed=

50900

s

2

m

2

=226

s

m

Hence, we have that the resultant speed of the plane is (3) 226 m/s