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:

1) Velocity = 132 m/sec

2) Direction angle = 24° South of West

Step-by-step explanation:

1) The speed with which the plane is flying, $v_{plane}$ = 120 m/sec

The direction in which the plane is flying = Due West

The speed of the blowing strong wind, $v_{wind}$ = 54 m/s

The direction of the strong wind = Due South

The vector form of the given velocities are;

$v_{plane}$ = -120·i

$v_{wind}$ = 54·j

The resultant velocity in vector format, $\underset{\textbf{v}}{\rightarrow}$ is given as follows;

$\underset{\textbf{v}}{\rightarrow}$ = -120·i + 54·j

Therefore, the magnitude of the resultant velocity, $\left |\underset{v}{\rightarrow} \right |$, is given as follows;

$\left |\underset{v}{\rightarrow} \right |$ = √((-120)² + (54)²) = 131.590273197

∴ The magnitude of the plane's resultant velocity, $\left |\underset{v}{\rightarrow} \right |$ ≈ 132 m/sec, when rounded to the nearest whole number

2) The direction angle of the plane's resultant velocity, θ, is given as follows;

$\theta = arctan \left ( \dfrac{\left |v_{wind}\right |}{\left |v_{plane}\right |} \right)$

Therefore, by substituting the known values, we have;

$\theta = arctan \left ( -\dfrac{54}{120} \right) = -24.227745317954169522385424019918 ^{\circ}$

∴ By rounding to the nearest whole number, the direction angle of the plane's resultant velocity = θ ≈ -24° = 204° which is 24° South of West.