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)

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, = 120 m/sec

The direction in which the plane is flying = Due West

The speed of the blowing strong wind, = 54 m/s

The direction of the strong wind = Due South

The vector form of the given velocities are;

= -120·i

= 54·j

The resultant velocity in vector format, is given as follows;

= -120·i + 54·j

Therefore, the magnitude of the resultant velocity, , is given as follows;

= √((-120)² + (54)²) = 131.590273197

∴ The magnitude of the plane's resultant velocity, ≈ 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;

Therefore, by substituting the known values, we have;

∴ 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.

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step-by-step explanation: