An airplane is traveling 25° west of north at 300 m/s when a wind with velocity 100 m/s directed 35° east of north begins to blow. using graphical methods, determine the magnitude and direction of the resultant velocity.

The resultant velocity is 360.5 m/s  and direction 79° north of east.

Explanation:

Given that,

Velocity of airplane = 300 m/s

Velocity of wind = 100 m/s

Angle θ₁ = 25°

Angle θ₂ =35°

The horizontal velocity component

Using formula of velocity

Put the value into the formula

The vertical velocity component

Using formula of velocity

Put the value into the formula

We need to calculate the resultant velocity

Using formula of resultant velocity

Put the value into the formula

We need to calculate the direction of the resultant velocity

Using formula of direction

Put the value into the formula

Hence, The resultant velocity is 360.5 m/s  and direction 79° north of east.

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