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) = √(365^2 + 136.73^2 - 2* 365* 136.73*cos22)</p><p>[tex]v_(plane) = 243.7 km/hr`

so above is the speed of the plane