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A plane flying due west at 120 m/sec is blown due south at 54 m/sec. by a strong wind. Find the plane’s resultant velocity and direction angle as a degree.
velocity = ___ m/sec (round answer to nearest whole number)


Direction angle = ____ ° (round answer to nearest whole number)

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boffeemadrid

Answer:

[tex]131.6\ \text{m/s}[/tex]

[tex]24^{\circ}[/tex]

Step-by-step explanation:

p = Velocity of plane = 120 m/s

w = Velocity of wind = 54 m/s

The resultant vector is

[tex]r=\sqrt{p^2+w^2}\\\Rightarrow r=\sqrt{120^2+54^2}\\\Rightarrow r=131.6\ \text{m/s}[/tex]

The resultant is [tex]131.6\ \text{m/s}[/tex]

Angle is given by

[tex]\theta=\tan^{-1}\dfrac{54}{120}\\\Rightarrow \theta=24.23^{\circ}\approx 24^{\circ}[/tex]

The direction angle is [tex]24^{\circ}[/tex]

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