Question

A plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph. after sometime and flight, space the plane encounters a 35 mph wind blowing directly north. Find the speed of the airplane after it encounters the wind.
A.322mph B.330mph C.285mph D.355mph

Answer 1

The speed of the plane after it encounters the wind is C.285mph

How to calculate the speed of the plane when it encounters the wind?

Since the plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph it's velocity is v = (320cos270°)i + (320sin270°)j

= (320 × 0)i + (320 × -1)j

= 0i - 320j

= - 320j mph

Also, the plane encounters a 35 mph wind blowing directly north. The velocity of the wind is v' = 35j mph

So, the velocity of the plane after it encounters the wind is the resultant velocity, V = v + v'

= -320j mph + 35j mph

= -285j mph

So, the speed of the plane after it encounters the wind is the magnitude of V = |-285j| mph

= 285 mph

So, the speed of the plane after it encounters the wind is C.285mph

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