Question

An airplane is flying in the direction of 43° east of north (also abbreviated as n43e) at a speed of 550 mph. A wind with speed 25 mph comes from the southwest at a bearing of n15e. What are the ground speed and new direction of the airplane?

a) Ground speed: 564 mph, New direction:
b) Ground speed: 575 mph, New direction: n28e
c) Ground speed: 525 mph, New direction: n58e
d) Ground speed: 525 mph, New direction: n28e

Answer 1

To find the ground speed and new direction of the airplane, we can use vector addition. The ground speed is approximately 564 mph and the new direction is n28e.

Step-by-step explanation:

To find the ground speed and new direction of the airplane, we can use vector addition. The airplane has a velocity of 550 mph in the direction n43e, and the wind has a velocity of 25 mph in the direction n15e. We can break down these velocities into their components. The velocity of the airplane in the north direction is 550 * sin(43) mph and in the east direction is 550 * cos(43) mph. Similarly, the velocity of the wind in the north direction is 25 * sin(15) mph and in the east direction is 25 * cos(15) mph. By adding these components, we can find the total velocity of the airplane relative to the ground. The ground speed is the magnitude of this total velocity. The new direction can be found by taking the inverse tangent of the ratio of the north and east components.

Using these calculations, we find that the ground speed of the airplane is approximately 564 mph and the new direction is n28e.