Question

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.

Answer 1

Answer:

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

$v_{x}=v_{1}\cos\theta-v_{2}\cos\theta$

Put the value into the formula

$v_{x}=300\cos65-100\cos55$

$v_{x}=69.42\ m/s$

The vertical velocity component

Using formula of velocity

$v_{y}=v_{1}\sin\theta+v_{2}\sin\theta$

Put the value into the formula

$v_{y}=300\sin65+100\sin55$

$v_{y}=353.8\ m/s$

We need to calculate the resultant velocity

Using formula of resultant velocity

$v=\sqrt{v_{x}^2+v_{y}^2}$

Put the value into the formula

$v=\sqrt{69.42^2+353.8^2}$

$v=360.5\ m/s$

We need to calculate the direction of the resultant velocity

Using formula of direction

$\tan\theta=\dfrac{v_{y}}{v_{x}}$

Put the value into the formula

$\theta=\tan^{-1}(\dfrac{353.8}{69.42})$

$\theta=79^{\circ}$

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