# Vectors and Two Dimensional Motion

• Eagleq8
In summary: You don't know. You just have to make your best guess. For what it's worth, I think it's a poorly worded question. I would move...In summary, the velocity of an airplane is 425 km/h, in a direction of 40 degrees north of east. The wind is blowing at a velocity of 75 km/h northward. It takes the plane 2000 km to make a displacement of 2000 km.
Eagleq8

## Homework Statement

The velocity of an airplane is 425 km/h, in a direction of 40 degrees north of east. The wind is blowing at a velocity of 75 km/h northward.
A. What is the resultant velocity of the plane?
B. How long does it take for the plane to make a displacement of 2000 km?

## Homework Equations

Horizontal component: Rx=Rcosθ
Vertical component: Ry=Rsinθ
Velocity resultant: √(Rx)^2+(Ry)^2
Direction: tanθ=Ry/Rx
Time: Δt=Δx/v

## The Attempt at a Solution

I split the plane and wind vectors to Rx and Ry and calculated the total Rx and total Ry. Then I calculated the Resultant Velocity and the Direction.
My problem is in the second requirement. I used the formula Δt=Δx/v. What velocity should I use here? Should I use the Horizontal or Vertical or Resultant Velocity(from the first requirement) to find the time?

Eagleq8 said:
My problem is in the second requirement. I used the formula Δt=Δx/v. What velocity should I use here? Should I use the Horizontal or Vertical or Resultant Velocity(from the first requirement) to find the time?

What do you think?

PeroK said:
What do you think?
The resultant velocity?

Eagleq8 said:
The resultant velocity?

What else?

PeroK said:
What else?
What do you mean? Sorry I am not good in physics :p

Eagleq8 said:
What do you mean? Sorry I am not good in physics :p

Resultant velocity is velocity. The others are just components. The overall displacement depends on the overall velocity.

PeroK said:
Resultant velocity is velocity. The others are just components. The overall displacement depends on the overall velocity.
Aha I see. Thanks ^^

Eagleq8 said:
Aha I see. Thanks ^^

I should add that the question would have been better if it emphasised that you are given the airspeed of the aircraft (i.e. the velocity relative to the air) and the velocity of the air relative to the ground and the required resultant velocity of the aircraft is relative to the ground.

In addition, the required displacement of the aircraft is relative to the ground.

PeroK said:
I should add that the question would have been better if it emphasised that you are given the airspeed of the aircraft (i.e. the velocity relative to the air) and the velocity of the air relative to the ground and the required resultant velocity of the aircraft is relative to the ground.

In addition, the required displacement of the aircraft is relative to the ground.
I see. Sorry but I just want to make sure, even though I am given the airspeed of the aircraft which is 425 km/h I should still use the resultant velocity instead of the given one because the wind changes the speed of the aircraft right?

Eagleq8 said:
I see. Sorry but I just want to make sure, even though I am given the airspeed of the aircraft which is 425 km/h I should still use the resultant velocity instead of the given one because the wind changes the speed of the aircraft right?

The wind means that the ground speed of the aircraft is different from its airspeed.

Here's how I interpreted your question.

The velocity of an airplane (relative to the air) is 425 km/h, in a direction of 40 degrees north of east. The wind is blowing at a velocity of 75 km/h northward.
A. What is the resultant velocity of the plane (relative to the ground)?
B. How long does it take for the plane to make a displacement of 2000 km (relative to the ground)?

So I still should use the resultant velocity which is the ground speed of the aircraft instead of the given velocity which is the airspeed of the aircraft, in order to find the time it takes for the aircraft to make a displacement of 2000 km. correct?

Eagleq8 said:
So I still should use the resultant velocity which is the ground speed of the aircraft instead of the given velocity which is the airspeed of the aircraft, in order to find the time it takes for the aircraft to make a displacement of 2000 km correct?

See above. If the displacement is relative to the ground, then yes.

PeroK said:
See above. If the displacement is relative to the ground, then yes.
How do I know if the displacement is relative to the ground? The question is literally the same as what I typed at the top of the post(to find the time it takes for the plane to make a displacement of 2000 km)

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Eagleq8 said:
How do I know if the displacement is relative to the ground? The question is literally the same as what I typed at the top of the post(to find the time it takes for the plane to make a displacement of 2000 km)

You don't know. You just have to make your best guess. For what it's worth, I think it's a poorly worded question. I would move on.

PeroK said:
You don't know. You just have to make your best guess. For what it's worth, I think it's a poorly worded question. I would move on.
Yeah true there are many poorly worded questions. So just to round it up so I can solve it and show the teacher. I should just use the resultant velocity right?

Notwithstanding the question isn't precisely worded, it makes little sense to ask "what's the displacement relative to the patch of air the aircraft went through 2000km ago".

Last edited:

## 1. What is a vector?

A vector is a quantity that has both magnitude (size or length) and direction. It is represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.

## 2. How is a vector different from a scalar?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include time, mass, and temperature, while examples of vectors include displacement, velocity, and force.

## 3. How are vectors represented mathematically?

Vectors are typically represented using coordinates, where the x and y components represent the horizontal and vertical directions, respectively. They can also be represented using magnitude and direction, using trigonometric functions such as sine and cosine.

## 4. What is two-dimensional motion?

Two-dimensional motion refers to the movement of an object in two directions, typically horizontal and vertical. This can be represented using vectors, where the x component represents the horizontal motion and the y component represents the vertical motion.

## 5. Can vectors be added or subtracted?

Yes, vectors can be added or subtracted using the parallelogram law. This involves placing the tail of one vector at the head of the other vector, and the resultant vector will be the diagonal of the parallelogram formed by the two vectors. This is known as vector addition. Vector subtraction involves adding the negative of the second vector to the first vector.

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