A truck is moving at a speed of 70km/h. The exhaust pipe above the truck cab sends out a trail of smoke that makes an angle of
20o
east of south behind the truck. If the wind is blowing directly toward the east, what is the wind speed at that location?
In what direction is the truck moving, due south, south-west?
Answers will vary depending on the direction.
is not given in the question
We assume that the wind is blowing east at x km/h, represented by the vector <x,0>
The truck is moving along the vector <p,q>, where sqrt(p²+q²)=70 km/h, or <sqrt(70²-q²), q>
We also know that the resultant of the two velocities equals <u,v> where
tan(-70°)=u/v.
Combining all information, we have:
resultant velocity of smoke
=<u,v>
=<x,0>+<sqrt(70²-q², q)
=<x+sqrt(70²-q²), q>
where
tan(-70°)=u/v
=(x+sqrt(70²-q²)) / q
Solve for x when q is known.
25.4779
A truck is moving north at speed of 70km/h. The exhaust pipe above the truck cab sends out a trail of smoke that make an angle of 20degree east of south behind the truck. If the wind os blowing directly towards the east what is the wind speed at that location
To find the wind speed at the given location, we need to break down the velocity vectors of the truck and the wind. Here's how we do it:
1. Draw a diagram: Draw a coordinate system with the positive y-axis pointing north and the positive x-axis pointing east. Label the truck position as point A and the location of the exhaust pipe smoke as point B. The exhaust trail makes an angle of 20° east of south behind the truck, so draw a line from point A towards the south, and then rotate it 20° towards the east.
2. Determine the velocity of the truck: The speed of the truck is given as 70 km/h. Convert this speed to m/s by dividing by 3.6 (1 km/h = 1/3.6 m/s). So, the velocity of the truck (V_truck) is (70/3.6) m/s.
3. Determine the components of the truck's velocity: Since the exhaust trail is angled relative to south, we need to determine the component of the truck's velocity in the south and east directions. The south component (V_south) is calculated by multiplying the magnitude of the velocity by the sine of the angle (20°). The east component (V_east) is calculated by multiplying the magnitude of the velocity by the cosine of the angle.
V_south = V_truck * sin(20°)
V_east = V_truck * cos(20°)
4. Determine the velocity of the wind: Since the wind is blowing directly toward the east, its velocity is purely in the east direction. Let's call this velocity V_west (since it is in the opposite direction to the positive east axis).
5. Determine the net velocity of the smoke: The net velocity of the exhaust trail is the sum of the velocities of the truck and the wind. Since the smoke trail is observed to be moving towards the south-east direction, the net velocity (V_net) can be written as:
V_net = V_south + V_east + V_west
6. Determine the magnitude of the wind speed: Since we know the net velocity of the smoke and the components of the truck's velocity, we can solve for the magnitude of the wind speed. To do this, we need to consider only the east component of the net velocity (V_net_east). The magnitude of the wind speed (V_wind) is then given by:
V_wind = V_net_east - V_east
Note: We subtract the east component of the truck's velocity (V_east) since the wind is blowing in the opposite direction.
Now, you can substitute the given values and calculate the wind speed at that location.