Question
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?
20o
east of south behind the truck. If the wind is blowing directly toward the east, what is the wind speed at that location?
Answers
MathMate
In what direction is the truck moving, due south, south-west?
Answers will vary depending on the direction.
Answers will vary depending on the direction.
samson
is not given in the question
MathMate
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.
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.
Jomar
25.4779
Usman jibril
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