Question

An airplane is flying through the air at a speed of 150 mph at a heading of 60 degrees. if the wind is blowing at 20 mph from the south-east, (a) what is its ground speed, and (b) how far and (c) in what direction from its starting point will the plane be located after flying for 30 minutes.

Answer 1

Step-by-step explanation:

Given

speed of plane 150 mph

heading
`60^(\circ)`

wind is blowing at 20 mph from south-east

velocity of plane w.r.t. wind

`v_(pw)=150(\cos 60\hat{i}+\sin 60\hat{j})`

`v_(w)=20(\cos 45\hat{i}-\sin 45\hat{j})`

`v_(p)=v_(pw)+v_(w)`

`v_(p)=(150\cos 60+20\cos 45)\hat{i}+(150\sin 60-20\sin 45 )\hat{j}`

`v_(p)=89.14\hat{i}+115.76\hat{j}`

`|v_(p)|=146.103 m/s`

(b)after 30 minutes

Plane traveled in x direction
`=89.14* 0.5=44.57 miles`

Plane in Y direction
`=115.76* 0.5=57.88 miles`

Total distance
`=√(x^2+y^2)=73.05 miles`

direction
`tan\theta =(115.76)/(89.14)=1.298`

`\theta =52.38^(\circ)` w.r.t east