Need some help on vector question

  • Thread starter krypt0nite
  • Start date
  • Tags
    Vector
In summary, the plane traveling due north at 300 km/h was blown off course by a southwest wind at an average speed of 50 km/h. After 30 minutes, it was 25 km northeast of its intended position, with a distance of 17.6 km from its intended east-west path. In a separate scenario, an automobile traveling at 90 km/h overtakes a train on a parallel track moving at 60 km/h. In the same direction, the car will take 0.033 hours to pass and travel 3 km, while in opposite directions, it will take 0.0067 hours to pass and travel 0.6 km. The distances traveled by the car and train differ due to the
  • #1
krypt0nite
31
0
An airplane is heading due north at a speed of 300km/h. If a wind begins blowing from the southwest at a speed of 50km/h(average), calculate (a) the velocity (magnitude and direction) of the plane, and (b) how far off course it will be in 30 min.

Ok, I solved a) 337km/h 6 degrees E of N.
But I dont' understand how to solve part b.
Anyone want to help?
 
Physics news on Phys.org
  • #2
The plane intended to be moving due north at 300 km/hr, so it should be 150 km due north after 30 minutes.

The wind blew it off-course, however, and it actually moved 337/2 km, six degrees east of north.

Draw a triangle, one leg pointing due north with length 150, another leg pointing six degrees east of north with length 337/2 (168.5), then solve for the length of the third leg. The length of the third leg is the distance between the plane's intended and actual positions after 30 minutes.

- Warren
 
  • #3
i got 24.8km but the answer sheet says 17.6km. :frown:
 
  • #4
It depends on what you mean by "how far off course". If you think about it, at the end of half an hour the plane will be 25 kilometers due northeast of where it should be. This is the result of the 300 kph of the plane's still-air speed plus the 50 kph due northeast from the wind. Clearly, the only thing moving the plane off course is the wind.

If you decompose the vectors, you have an isosceles right triangle with hypotenuse 25 km, making the legs 17.6 km. So, one could argue that it's only 17.6 km east of where it should be, and 17.6 km north of where it should be.
 
  • #5
Okay, guys I need help on another question.

An automobile traveling 90km/h, overtakes a 1.0km train traveling the same direction on a track parallel to the road. If the train's speed is 60km/h, how long does it take the car to pass it and how far will it have traveled in this time? What are the results if the car and train are traveling in opposite directions?

Same Direction: t=.033hours d=3 km
Opposite Direction t=.0067 hour d=.6 km

I don't understand why my distances are wrong. My times are correct though.
The answers are d=2km for same direction and d=.4km for opposite direction.

Can anyone explain this to me?
 
  • #6
Displaying how you derived your results would be much more helpfull than telling "I got x=y" because it would save us the time to guess what you did.

However: In this case I think you calculated out how far the car traveled while the question was supposed to be how far the train travels (doesn´t seem obvious to me what´s asked for - as in your 1st question). Hence the factor 60/90 = 2/3 difference between your results and the book´s.

btw.: Your book (or teacher - whoever gave you the questions) suxx.
 

1. What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is commonly represented using an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

2. How do you add or subtract vectors?

To add or subtract vectors, you must first make sure that they are of the same dimension. Then, you can add or subtract the corresponding components of the vectors. For example, to add two 2-dimensional vectors, you would add their x-components and y-components separately.

3. What is the difference between a scalar and a vector?

A scalar is a mathematical object that only has magnitude (size) and no direction. On the other hand, a vector has both magnitude and direction. Scalars can be thought of as the "amount" of something, while vectors represent a quantity with both an amount and a direction.

4. How do you find the magnitude of a vector?

To find the magnitude of a vector, you can use the Pythagorean theorem. Suppose a vector has components (x, y), then its magnitude can be found using the formula: magnitude = √(x² + y²). Alternatively, you can also use the distance formula to find the magnitude of a vector.

5. Can vectors be multiplied?

Yes, vectors can be multiplied, but there are different types of vector multiplication. The dot product, also known as the scalar product, returns a scalar value. The cross product, on the other hand, returns a vector that is perpendicular to the two original vectors. There is also a type of multiplication called the outer product, which returns a matrix. These types of multiplication have various applications in physics and mathematics.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
829
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
4K
  • Introductory Physics Homework Help
3
Replies
72
Views
6K
  • Introductory Physics Homework Help
Replies
4
Views
687
  • Introductory Physics Homework Help
Replies
7
Views
1K
Replies
1
Views
1K
Back
Top