An airplane with an airspeed of 120 km/h has a heading of 30° east of north in a wind that is blowing toward the west at 30 km/h.What is the speed of the plane relative to the ground?
A)90 km/h
B)110 km/h
C)140 km/h
D)150 km/h

Question

Quizplus · Accepted Answer

To find the speed of the plane relative to the ground, we need to use vector addition. The airspeed of 120 km/h with a heading of 30° east of north can be represented as two components: 60 km/h northward and 104.4 km/h eastward (using trigonometry).

Next, we need to add the velocity due to the wind blowing toward the west at 30 km/h. Since this is in the opposite direction of the plane's heading, we subtract it from the plane's velocity. This gives us a resultant velocity of 74.4 km/h northward and 104.4 km/h eastward.

Using the Pythagorean theorem, we can find the magnitude of this resultant velocity:

sqrt((74.4 km/h)^2 + (104.4 km/h)^2) = 127 km/h (rounded to the nearest km/h)

Therefore, the speed of the plane relative to the ground is 127 km/h. However, the question asks for the answer to the nearest 10 km/h, so we round this to 130 km/h. The closest answer choice is B) 110 km/h, which is not the exact answer, but it is the best choice given in the options.

An Airplane with an Airspeed of 120 Km/h Has a Heading