Trucks travels beneath an airplane .

[ArcherofScience]

trucks travels beneath an airplane...

Homework Statement

A truck travels beneath an airplane that is
moving 180 km/h at an angle of 39 to the
ground. How fast must the truck travel to stay be-
neath the airplane? What is the magnitude of the vertical component of the velocity of the plane? Answer in units of km/h

Homework Equations

My physics teacher said the question is identifying the horizontal and vertical components. So I had to do Vcostheta and Vsintheta.

The Attempt at a Solution

Vcostheta=180cos39=139.8863 km/h
vsintheta=180sin39=113.2777 km/h

my problem is, I don't understand which direciton the vectors are. Is it going north of east or south of east, or what? I can't identify them in the problem and I can't tell if the answers need a negative sign or positive sign.

 

[Dick]

Homework Statement

A truck travels beneath an airplane that is
moving 180 km/h at an angle of 39 to the
ground. How fast must the truck travel to stay be-
neath the airplane? What is the magnitude of the vertical component of the velocity of the plane? Answer in units of km/h

Homework Equations

My physics teacher said the question is identifying the horizontal and vertical components. So I had to do Vcostheta and Vsintheta.

The Attempt at a Solution

Vcostheta=180cos39=139.8863 km/h
vsintheta=180sin39=113.2777 km/h

my problem is, I don't understand which direciton the vectors are. Is it going north of east or south of east, or what? I can't identify them in the problem and I can't tell if the answers need a negative sign or positive sign.

The problem is only asking you questions like "How fast" and "magnitude of". Those are questions where the answer is always positive. You can pick a direction for things to be traveling in if it helps you picture things but it shouldn't affect your answer.

 

[ArcherofScience]

ohh ok. i see. thanks :)...i have another question from my hw...is it ok to ask it on this same thread?

 

[Dick]

ohh ok. i see. thanks :)...i have another question from my hw...is it ok to ask it on this same thread?

Its ok. But it will probably get more attention if you post it in a new thread.

 

[Nickie]

As a scientist, it is important to clarify the direction of vectors in a problem. In this case, we can assume that the airplane is moving towards the east, as this is the most common direction for airplanes to travel. Therefore, the horizontal component of the airplane's velocity would be positive, and the vertical component would be negative.

To determine the speed at which the truck must travel to stay beneath the airplane, we can use the Pythagorean theorem. The magnitude of the airplane's velocity can be found using the horizontal and vertical components:

Vplane = √(Vcosθ)^2 + (Vsinθ)^2
= √(180cos39)^2 + (180sin39)^2
= 180 km/h

Since the truck needs to travel at the same speed as the airplane, its velocity would also be 180 km/h. However, the direction of the truck's velocity would depend on the angle at which it is traveling relative to the airplane's direction.

To calculate the magnitude of the vertical component of the airplane's velocity, we can use the equation Vsinθ:

Vvertical = Vsinθ
= 180sin39
= 113.2777 km/h

Therefore, the vertical component of the airplane's velocity is 113.2777 km/h.

In summary, to stay beneath the airplane, the truck would need to travel at a speed of 180 km/h in the same direction as the airplane. The magnitude of the vertical component of the airplane's velocity is 113.2777 km/h.