A plane has an airspeed of 200 m/s northward,and is in a wind of 50.0 m/s to the west.The plane's speed relative to the ground is
A)150 m/s.
B)200 m/s.
C)206 m/s.
D)250 m/s.

Question

Quizplus · Accepted Answer

To find the plane's speed relative to the ground, we need to use vector addition. We can draw a diagram where the plane's airspeed is one vector pointing north (let's call it A), and the wind speed is another vector pointing west (let's call it B). The resulting vector (let's call it C) will be the plane's speed relative to the ground.

To add these vectors, we can use the Pythagorean theorem to find the length of the hypotenuse (C) of a right triangle formed by vectors A and B:

C = sqrt(A^2 + B^2)

Plugging in the values, we get:

C = sqrt(200^2 + 50^2)
C = sqrt(40,000 + 2,500)
C = sqrt(42,500)
C ≈ 206.15

So the plane's speed relative to the ground is approximately 206 m/s, which is closest to answer choice C.

A Plane Has an Airspeed of 200 M/s Northward,and Is