Question

2. An airplane traveling north at 220. meters per second encounters a 50.0-meters-per-second crosswind
from west to east, as represented in the diagram below.
What is the resultant speed of the plane?
(1) 170. m/s
(2) 214 m/s
(3) 226 m/s
(4) 270. m/s
220. m/s
50.0 m/s​

Answer 1

The resultant speed of the plane  is (3) 226 m/s

Why?

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:

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

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

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

Have a nice day!

Answer 2

The resultant of the speed of the plane is 226 m/s.

The given parameters;

• initial velocity of the plane, u = 220 m/s north
• velocity of the crosswind, v = 50 m/s west

The resultant of the speed of the plane is calculated by applying Pythagoras theorem as shown below;

R = 220² + 50²

R = 50900

R = √50900

R = 225.61 m/s

R ≈ 226 m/s.

Thus, the resultant of the speed of the plane is 226 m/s.

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