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

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

Step-by-step 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=√(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=(v_(y))/(v_(x))`

Put the value into the formula

`\theta=\tan^(-1)((353.8)/(69.42))`

`\theta=79^(\circ)`

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