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?
What is the formula and how would you work it out?
Thank you!
You are welcome.
1.c
2.c
3.a
4.d
5.d
6.c
7. they are equal
8 A.a
8 B.d
9 A. c
9 B. b
10 A.c
10 B. b
11.b
12.d
13.b
14.b
15. a
16.d
17.c
18. 26.56 degrees
To determine the actual velocity of the plane, we can use vector addition since both the plane's velocity and the wind's velocity are in different directions.
The formula for vector addition is:
Resultant velocity = Velocity of the plane + Velocity of the wind
Now, let's work it out step by step:
1. Start by identifying the magnitudes and directions of the velocities:
- Velocity of the plane = 150 mph (due east)
- Velocity of the wind = 50 mph (due south)
2. Convert the velocities into vector form:
- Velocity of the plane = 150 mph (0i + 150j) (i represents the x-axis, and j represents the y-axis)
- Velocity of the wind = 50 mph (0i - 50j)
3. Add the vectors together:
Resultant velocity = (0i + 150j) + (0i - 50j)
= 0i + (150j - 50j)
= 0i + 100j
= (0i + 100j)
4. The resultant velocity vector (0i + 100j) implies that the plane is traveling north at a rate of 100 mph. Since the original question asked for the actual velocity of the plane, we can conclude that the actual velocity of the plane is 100 mph due north.
Therefore, the actual velocity of the plane is 100 mph due north.
V^2 = 150^2 + 50^2
V =