AMDM Constructed Response Question (Mathematics)

Question

A plane traveling at 300 mph is flying with a bearing of 30°. There is a wind of 50 mph from the south. If no correction is made for the wind, what are the final bearing and ground speed of the plane?

Answer 1

A plane traveling at 300 mph is flying with a bearing of 30°. There is a wind of 50 mph from the south. If no correction is made for the wind, what are the final bearing and ground speed of the plane?

Compose vectors to represent both the planes velocity, and that of the wind:

Plane velocity <x,y> in component form ASSUMING 30° East of North = < 300cos60 , 300 sin60 >

Wind velocity coming "from the South" = < 0 , +50 >

Sum the vectors to get the planes ground speed in <x,y> component form:

= < 300cos60 , +50 + 300sin60 >

= < 150, 309.8 >

Use √(x² + y²) to get speed:

= √(150² + 309.8²)

Ground Speed = 344.2 mph

Use θ = tan^-1(309.8/150) = 64.16 degrees

Bearing θ = 25.86° East of North