Define an x-y coordinate system such that
The positive x-axis = the eastern direction, with unit vector

.
The positive y-axis = the northern direction, with unit vector

.
The airplane flies at 340 km/h at 12° east of north. Its velocity vector is

The wind blows at 40 km/h in the direction 34° south of east. Its velocity vector is
![\vec{v}_{2} =40(cos(34^{o})\hat{i} - sin(24^{o})]\hat{j}) = 33.1615\hat{i} -22.3677\hat{j})](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D_%7B2%7D%20%3D40%28cos%2834%5E%7Bo%7D%29%5Chat%7Bi%7D%20-%20sin%2824%5E%7Bo%7D%29%5D%5Chat%7Bj%7D%29%20%3D%2033.1615%5Chat%7Bi%7D%20-22.3677%5Chat%7Bj%7D%29)
The plane's actual velocity is the vector sum of the two velocities. It is

The magnitude of the actual velocity is
v = √(121.1615² + 306.0473²) = 329.158 km/h
The angle that the velocity makes north of east is
tan⁻¹ (306.04733/121.1615) = 21.6°
Answer:
The actual velocity is 329.2 km/h at 21.6° north of east.
Because gas particles in the air like particles of all fluids are constantly moving and bumping into things, they exert pressure. The pressure exerted by the air in the atmosphere is greater close to Earth's surface and decreases as you go higher above the surface.
<u>Explanation</u>:
- Fill roughly one-third of a cup with water. Then, cover the mouth of the cup completely with a flat, hard cardboard. Using your hand to keep it in place, turn the cup upside down. When you remove your hand, the the cardboard stays in place.
-
One would expect that due to gravity, the water will fall, and even the cardboard will. However, it does not, which means that something must be applying an upward force on the cardboard. This is nothing other than air pressure, which applies a force across the surface of the cardboard in an upward direction.
- Thus we can demonstrate that air exerts pressure, because otherwise, the water would have fallen.
Answer:
The force experienced is 375 N.
Explanation:
Here,
Mass of the object( M)= 75 kg
Acceleration of the body(a) =5 m/s²
Force required to accelerate the body( F) =?
Then, we know ,
From newton's second law of motion,

=
=375 kgm/s²
= 375 Newton
So, The force experienced by the 75 kg body that undergoes an acceleration of 5 m/s² is 375 N.
Answer:
Coefficient of static friction required = 0.94
Explanation:
Coefficient of static friction required 
Velocity, v = 120 km/h = 33.33 m/s
g = 9.81 m/s²
R = 120 m
Coefficient of static friction required
Coefficient of static friction required = 0.94
Answer:
ΔV = -2.1 L
Explanation:
To solve this exercise we can use the ideal gas equation for two points
PV = nRT
P₁V₁ = P₂ V₂
where point 1 is on the surface and point 2 is at the desired depth,
V₂ =
let's calculate
V₂ = (
) 3.5 L
V₂ = 1.4 L
this is the new volume, the change in volume is
ΔV = V₂ -V₁
ΔV = 1.4-3.5
ΔV = -2.1 L