A private plane is traveling due east at a rate of 150 mph. A south wind is blowing 50 mph. What is the actual velocity of the plane?
A. 141 mph
B. 158 mph
C. 172 mph
D. 200 mph
B. 158 mph
To find the actual velocity of the plane, we need to consider the wind speed as a vector in the opposite direction of the plane's velocity. The speed of the wind is 50 mph to the south.
Using the Pythagorean theorem, we can calculate the actual velocity of the plane:
Actual velocity = sqrt((150^2) + (50^2))
Actual velocity = sqrt(22500 + 2500)
Actual velocity = sqrt(25000)
Actual velocity = 158 mph
Therefore, the actual velocity of the plane is 158 mph.