A Plane flies north at 215 km/h. A wind from the east blows at 69km/h. What is the plane's new velocity with respect to the ground in standard position
X = -69 km/h
Y = 215 km/h
Tan Ar = Y/X = 215/-69 = -3.11594
Ar = -72.21o = Reference angle.
A = -72.21 + 180 = 107.8o
V=Y/sinA = 215/sin107.8=225.8km/h[107.8]
Henry... where did you get the reference angle from? -72.21??
Why Vx is negative (-69km/h)
To find the new velocity of the plane with respect to the ground, we can use vector addition. Since the plane is flying north and the wind is blowing from the east, we can treat their velocities as two vectors.
The north velocity of the plane is 215 km/h, and the east velocity of the wind is 69 km/h. We can represent these velocities as vectors:
Plane velocity (north) = 215 km/h north = 215i
Wind velocity (east) = 69 km/h east = 69j
Now, we need to add these two vectors to find the resultant velocity of the plane with respect to the ground. To do this, we can use vector addition:
Resultant velocity = Plane velocity + Wind velocity
So, (Resultant velocity) = (215i) + (69j)
To calculate this, we add the corresponding components of the vectors:
(Resultant velocity) = (215i + 0j) + (0i + 69j)
= 215i + 69j
Therefore, the plane's new velocity with respect to the ground in standard position is 215 km/h north and 69 km/h east.