Answer:
966.22 mph
Explanation:
Velocity of plane with respect to wind (Vp,w)= 612 mph east
velocity of wind with respect to ground, (Vw,g) = 362 mph at 15° North of
east
Write the velocities in vector form
Use the formula for the relative velocity
Where, V(p,w) is the velocity of plane with respect to wind
V(p,g) is the velocity of plane with respect to ground
V(w,g) is the velocity of wind with respect to ground
So,
Magnitude of velocity of lane with respect to ground
V(p,g) = 966.22 mph
Say the initial point is (0,0)
The final point is
x = 200 + 135*cos(30) = 200 + 135*sqrt(3)/2 = 316.91 ft
y = 135*sin(30) = 135/2 = 67.5 ft
Resultant vector = (316.91, 67.5) - (0,0) = 316.91, 67.5) ft
Answer:
C because you can test it your self
Answer:
a) 202.7 N
b) 58.1 N
c) 74.1º N of E.
d) 210.9 N
Explanation:
a)
- The net force exerted in the y-direction, will be the sum of FH (which is directed northwards) and the y-component of FA.
- Since the magnitude of FA is 155 N and the angle of FA with the y-axis, is 22º (E of N), we can find the N-S component of FA, just applying the the definition of cosine, to the triangle defined by FA, the y- axis and a segment parallel to the x- axis between FA and the y-axis, as follows:
⇒ Fy = FH + FAy = 59 N + 143.7 N = 202.7 N (2)
b)
- We can proceed exactly in the same way for the x-axis.
- Since FH is directed due North, it has no component along the x-axis.
- So, Fx is directly the component of FA along the x-axis, which can be found applying the definition of sine to the same triangle than in a) as follows:
c)
- Taking the same triangle than in a) and b), we can apply the definition of tangent, in order to find the angle between F and the x-axis, as follows:
⇒ θ = tg⁻¹ (3.5) = 74.1º N of E. (5)
d)
- In order to be equal and opposite to the combined force FH+FA, it must have the same magnitude.
- This magnitude can be found applying the Pythagorean Theorem to the same triangle that we used in a), b) and c):