Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocit
y of the plane and the velocity of the wind as vectors, using proper notation to represent each direction of motion. Part II: What is the velocity vector of the plane? Part III: What is the ground speed of the plane?
Define i as a unit vector in the eastern direction. Define j as a unit vector in the northern direction.
Part I Because the wind is blowing west, its velocity vector is -23i mph or as (-23, 0) mph Because the plane is traveling north, its velocity vector is 200j mph or as (0, 200) mph
Part II The actual velocity of the plane is the vector sum of the plane and wind velocities. That is, 200j - 23i or (-23, 200) mph
Part III The ground speed of the plane is the magnitude of its vector. The ground speed is √[200² + (-23)²] = 201.32 mph
The ground speed of the plane is 201.3 mph (nearest tenth)
Not: The direction of the plane is tan⁻¹ 23/200 = 6.56° west of north.
I multiplied .25(25%; Always change percent to decimal and always move it over 2 place) to $34.50 and got 8.625 but rounded it to get 8.63 and then added that to the normal cost and got $43.13.