A truck is moving north at a speed of 70kh/h. The exhaust pipe above the truck cab sends out a tail of smoke that makes an angle of 20degrees east or the south behind the truck. If the wind is blowing directly towards the east , what is the wind speed at that location?
I don't know
canned answer wrong again.
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Anonymous
Nov 3, 2021
#lien your heart out
To find the wind speed at the location, we need to analyze the motion of the smoke tail relative to the truck's motion and the wind's motion. Let's break down the problem step by step:
1. First, let's consider the motion of the truck. Given that the truck is moving north at a speed of 70 km/h, we know its velocity is directed straight north.
2. Next, let's analyze the motion of the smoke tail relative to the truck. The fact that the tail of smoke makes an angle of 20 degrees east of south means that it deviates from the truck's motion towards the east (right side) and slightly downwards.
3. Now, let's consider the wind's motion. Given that the wind is blowing directly towards the east, its velocity is directed straight east.
4. Combining the truck's velocity and the wind's velocity, we can determine the resultant velocity of the smoke tail relative to the ground. To do this, we can use vector addition.
a. The truck's northward velocity acts as a reference point. We can represent it as a vector pointing straight up.
b. The wind's eastward velocity can be represented as a vector pointing straight right.
c. The smoke tail's velocity is the resultant vector we are looking for. It will have a magnitude (speed) and direction.
5. To find the resultant of the truck's velocity and the wind's velocity, we can use trigonometry. The direction of the resultant vector will be the direction of the smoke tail.
a. Let's split the truck's velocity vector into two components: one in the northward direction (vertical) and one in the eastward direction (horizontal).
b. The horizontal component is zero because the truck's motion is purely vertical. The vertical component is 70 km/h.
c. To find the magnitude (speed) of the resultant vector, we can use trigonometry. The magnitude of the resultant vector can be calculated as the square root of the sum of the squares of the horizontal and vertical components. In this case, it will be 70 km/h.
d. To find the direction of the resultant vector, we can use trigonometry. The direction will be the angle between the horizontal component (eastward) and the resultant vector. Since the smoke tail is facing east of south, the angle will be 270 degrees (180 degrees for south + 90 degrees for east).
6. Finally, we subtract the wind's velocity from the resultant velocity to find the wind speed at that location. Since the wind's velocity is directed eastward, its magnitude will be equal to the horizontal component of the resultant velocity vector.
a. The horizontal component of the resultant velocity is the wind speed we are looking for.
b. In this case, the wind speed will be 0 km/h because the truck's motion cancels out the wind's eastward motion, resulting in no apparent wind speed.
Hence, the wind speed at that location is 0 km/h.