Question

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)

Answer 1

Answer:

$131.6\ \text{m/s}$

$24^{\circ}$

Step-by-step explanation:

p = Velocity of plane = 120 m/s

w = Velocity of wind = 54 m/s

The resultant vector is

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

The resultant is $131.6\ \text{m/s}$

Angle is given by

$\theta=\tan^{-1}\dfrac{54}{120}\\\Rightarrow \theta=24.23^{\circ}\approx 24^{\circ}$

The direction angle is $24^{\circ}$