Anovice pilot sets a plane’s controls, thinking the plane will fly at 2.50 × 102 km/h to the north. if the wind blows at 75 km/h toward the southeast, what is the plane’s resultant velocity? use graphical techniques.

The magnitude and direction of the resultant velocity of the airplane

obtained graphically are 201.43 km/hr in the direction  North 15.41° West,

The given parameters are;

Velocity of the plane, = 2.50 × 10² km/h

Direction of the plane = North

Velocity of the wind, = 75 km/h

Direction of the wind = Southeast

Required:

Resultant velocity of the plane

Solution:

Using graphical techniques, we have;

The direction of the plane relative to the x-axis is approximately 74.59°,

which is (90° - 74.59° ≈ 15.41°) North 15.41° West

By calculation, we have;

The component form of the given velocities are;

The resultant velocity is given by the sum of the two velocities as follows;

v = (75 × cos(45°) + 0)·i + (2.5×10² - 75 × sin(45°))·j ≈ 53.03·i + 196.97·j

The magnitude of the velocity, v = √(53.03² + 196.97²) ≈ 203.98

The plane resultant velocity, v ≈ 203.98 km/h

The direction of the resultant velocity, θ ≈

The magnitude and direction of the resultant velocity of the airplane are;

Therefore, there is a slight error in the values obtained graphically.

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Velocity of plane is given as

towards north

towards south east

we can write the two velocity in vector form

now the net velocity will be given as

so the resultant velocity will be given as

and the angle of velocity will be

explanation:

newton's third law, for every action there is an equal and opposite reaction.