Question

An airplane is pushed 22 degrees eastward off its northward course by a jet stream traveling at a speed of 136.73 km/hr. The new speed is 365 km/hr. Find the plane's original velocity.

Answer 1

As the speed of airplane is change due to jet stream

So the net speed is given as

$v_{net} = v_{plane} + v_{stream}$

now we can rearrange it as

$v_{plane} = v_{net} - v_{stream}$

now by the formula of vector difference we have

$v_{plane} = \sqrt{v_{net}^2 + v_{stream}^2 - 2v_{net}v_{stream}cos\theta}$

now plug in all values

$v_{plane} = \sqrt{365^2 + 136.73^2 - 2* 365* 136.73*cos22}[tex]v_{plane} = 243.7 km/hr$

so above is the speed of the plane