A pilot of a small plane wishes to fly west. The plane has an airspeed of 100 km/h. If
there is a 40-km/h wind blowing north, what is the plane’s ground speed?
a. 92 km/h
b. 94 km/h
c. 96 km/h
d. 98 km/h
To find the plane's ground speed, we can use vector addition.
Let the plane's velocity be represented by vector A (100 km/h) and the wind's velocity be represented by vector B (40 km/h north).
To find the resultant vector (ground speed), we need to add these two vectors together. Since they are perpendicular to each other, we can use the Pythagorean theorem:
Ground speed = sqrt((100)^2 + (40)^2)
Ground speed = sqrt(10000 + 1600)
Ground speed = sqrt(11600)
Ground speed ≈ 107.68 km/h
Therefore, the closest answer choice is:
c. 96 km/h