Solve Applied Maths Urgent Probl. 1: 20 Marks

In summary, the problem involves determining polar coordinate unit vectors ˆr and ˆθ for given Cartesian unit vectors and vectors, expressing them as a linear combination, and finding the polar coordinate unit vectors for a particle's motion described by a given position vector. The time derivative of the position vector is also mentioned in the problem.
  • #1
bilal98732
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Problem 1 20 marks (i) ˆx = (1, 0) and ˆy = (0, 1) are the Cartesian unit vectors and the vectors v1 and v2 are defined as v1 = −4ˆx + 0ˆy , v2 = 2ˆx − 7ˆy . Determine the polar coordinate unit vectors ˆr and ˆθ for v1 and v2 and hence express v1 and v2 as a linear combination of ˆr and ˆθ. [4]

(ii) A particle’s motion is described by the following position vector r(t) = αtxˆ + (βt2 − t)ˆy Determine the polar coordinate unit vectors ˆr and ˆθ for r. [4]

(iii) By differentiating with respect to time r(t), given in (ii) show that the velocity vector written in a Cartesian basis for this particle is v(t) = αxˆ + (2βt − 1)ˆy . [2] (iv) Using the ˆr and ˆθ you found in (ii) above, write v(t) as a linear combination of rˆ and ˆθ. [4]

(v) Differentiate the expression for r(t) you got in part (ii) (in terms of ˆr and ˆθ, and using the expressions ˙rˆ = ˙θ ˆθ , ˙ˆθ = − ˙θrˆ derived in the lectures, show that you obtain the same answer as in part (iv) [6]where r(vector) = r modulus * r
r^ = cos(pheta)x + sin(pheta)y
pheta^ = -sin(pheta)x +cos(pheta)yi am able to do i) and ii) but unbale to expres v(t) in terms of r and pheta
 
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  • #2
bilal98732 said:
Problem 1 20 marks (i) ˆx = (1, 0) and ˆy = (0, 1) are the Cartesian unit vectors and the vectors v1 and v2 are defined as v1 = −4ˆx + 0ˆy , v2 = 2ˆx − 7ˆy . Determine the polar coordinate unit vectors ˆr and ˆθ for v1 and v2 and hence express v1 and v2 as a linear combination of ˆr and ˆθ. [4]

(ii) A particle’s motion is described by the following position vector r(t) = αtxˆ + (βt2 − t)ˆy Determine the polar coordinate unit vectors ˆr and ˆθ for r. [4]
What did you get for the position vector?
What do you get when you take the time derivative of that expression?
 

1. What is the deadline for solving the applied math problem?

The deadline for solving the applied math problem is urgent, meaning it should be solved as soon as possible. The exact deadline may vary depending on the specific situation and urgency of the problem.

2. What are the specific requirements for solving the applied math problem?

The specific requirements for solving the applied math problem may vary, but typically they will involve using mathematical principles and techniques to analyze and solve a real-world problem. It is important to carefully read and understand the problem statement and any additional instructions provided.

3. How many marks is the applied math problem worth?

The applied math problem is worth 20 marks. This may also vary depending on the specific assignment or course requirements.

4. Can I use a calculator or other tools to solve the applied math problem?

This may depend on the specific instructions for the assignment or course. In some cases, a calculator or other tools may be allowed or even required. However, in other cases, the problem may be designed to be solved without the use of any external tools.

5. Is there any additional support or resources available for solving the applied math problem?

It is always a good idea to check with your instructor or classmates for any additional support or resources that may be available for solving the applied math problem. You may also find helpful resources online, such as math forums or tutorial websites.

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