Consider an object moving in two dimensions whose position vector at time t is given by...
Fantastic news! We've Found the answer you've been seeking!
Question:
![student submitted image, transcription available below](https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2023/09/650ad1c410aed_1695207876147.jpg)
![student submitted image, transcription available below](https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2023/09/650ad1c4ac7f7_1695207876356.jpg)
Transcribed Image Text:
Consider an object moving in two dimensions whose position vector at time t is given by 7 (t) = (-1², 21-1) for t 20 (a) Find expressions for the velocity vector v(t), ds the acceleration vector ä(t), and the speed dt +(1) (b) Find an expression for the tangential component of acceleration a, by applying the d's formula a, = dt (c) Find an expression for the unit tangent vector f(t). (ctd) (d) Find an expression for the tangential component of acceleration a, by applying the formula a, =ā Ť. Your answer should agree with part (b). (e) Compute ā (1), f(1), and a, (1). á (1) = f(1) = (f) Find a,, (1) using the formula a, (1)=√(1)-[a (1)]² a, (1) = g) Find (1). (This should not require any tedious computation; note that in 2 dimensions, the vectors (-b, a) and (b.-a) are the only two vectors that are both orthogonal to (a, b) and equal in length to (a, b). This makes it easy to find N if † is already known, provided you can figure out which of these two vectors to choose. Look at the figure at the beginning of the problem for guidance; remember that N always points toward the concave side of the curve.) (h) Using the formula a(t)= a,f(t)+a,Ñ(t), use the answers you have obtained thus far to express a (1) as a linear combination of f(1) and N(1). As a final check on your work, the two sides of the resulting equation should be in agreement. Consider an object moving in two dimensions whose position vector at time t is given by 7 (t) = (-1², 21-1) for t 20 (a) Find expressions for the velocity vector v(t), ds the acceleration vector ä(t), and the speed dt +(1) (b) Find an expression for the tangential component of acceleration a, by applying the d's formula a, = dt (c) Find an expression for the unit tangent vector f(t). (ctd) (d) Find an expression for the tangential component of acceleration a, by applying the formula a, =ā Ť. Your answer should agree with part (b). (e) Compute ā (1), f(1), and a, (1). á (1) = f(1) = (f) Find a,, (1) using the formula a, (1)=√(1)-[a (1)]² a, (1) = g) Find (1). (This should not require any tedious computation; note that in 2 dimensions, the vectors (-b, a) and (b.-a) are the only two vectors that are both orthogonal to (a, b) and equal in length to (a, b). This makes it easy to find N if † is already known, provided you can figure out which of these two vectors to choose. Look at the figure at the beginning of the problem for guidance; remember that N always points toward the concave side of the curve.) (h) Using the formula a(t)= a,f(t)+a,Ñ(t), use the answers you have obtained thus far to express a (1) as a linear combination of f(1) and N(1). As a final check on your work, the two sides of the resulting equation should be in agreement.
Expert Answer:
Answer rating: 100% (QA)
Lets break this down step by step a Find expressions for the velocity vector overlinevt the accelera... View the full answer
Related Book For
Posted Date:
Students also viewed these finance questions
-
Gold has a spot price of $3650 and the four month futures price is $3545. The four month continuously compounded risk-free interest rate is 4.5 per cent per year. The storage costs for Gold is 1.5...
-
Kubin Company s relevant range of production is 2 7 , 0 0 0 to 2 9 , 0 0 0 units. When it produces and sells 2 8 , 0 0 0 units, its average costs per unit are as follows: Average Cost per UnitDirect...
-
Instructions NOTE: Documentation and Conventions include the conventions for creating and formatting a newsletter, and the conventions of documenting sources in the text and at the end of the text on...
-
A chef in a restaurant that specializes in pasta dishes was experiencing difficulty in getting brands of pasta to be al dente-that is, cooked enough so as not to feel starchy or hard but still feel...
-
1. Is Jim headed for trouble? What would be some physical, psychological, and behavioral outcomes of this type of job stress? 2. What could the company do to help reduce the stress in Jims job? 3....
-
A potential difference V drives a steady current I through an ohmic wire with conductivity and a constant circular cross section. One portion of the wire has the shape of a circular arc with inner...
-
Describe Porters four generic business strategies.
-
Activity-based costing, batch-level variance analysis. Jo Nathan Publishing Company specializes in printing specialty textbooks for a small but profitable college market. Due to the high setup costs...
-
Roy purchased a Remington bronze sculpture for 35,000 seven years ago when it was worth 75,000. Roy gifted the sculpture to irrevocable granted trust Roy is the owner of the trust, but the trust...
-
Cascade Company has four employees. All are paid on a monthly basis. The fiscal year of the business is June 1 to May 31. The accounts kept by Cascade include the following: .:. The following...
-
1. What are institutional voids? What effects do institutional voids have on how business is conducted in societies? 2. Discuss three of Hofstedes national culture dimensions. What are some of the...
-
Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the P-value method or the traditional method of testing hypotheses. Company A...
-
Trojan Technologies As Joyce Guo, senior buyer at Trojan Technologies Inc. in London, Ontario, Canada, finished her presentation, Randy Haill, materials manager, Made the following comments to her:...
-
In 2022, Andrew, who is single, has a comfortable salary from his job as well as income from his investment portfolio. However, he is habitually late in filing his federal income tax return. He did...
-
Express the confidence interval (0.045,0.123) in the form of p^ - E < p < p^+ E.
-
Boomtown is preparing a cost analysis of the three departments: Parks. Fire, and Water. To comply with accuracy standards in allocating indirect costs, Boomtown will employ the step-down method of...
-
Last month 74,000 Kgs of direct material were purchased and 71,000 Kgs were used. If the actual purchase price per Kg was Rs.0.50 more than the standard purchase price per Kg, then what would be the...
-
(a) Find the equation of the tangent line to f(x) = x 3 at the point where x = 2. (b) Graph the tangent line and the function on the same axes. If the tangent line is used to estimate values of the...
-
A water line is to be built from point P to point S and must pass through regions where construction costs differ (see figure). The cost per kilometer (in dollars) is 3k from P to Q, 2k from Q to R,...
-
In Exercises verify that the general solution satisfies the differential equation. Then find the particular solution that satisfies the initial condition(s). y = e2x/ (C + C2x) 9y" 12y + 4y = 0 y = 4...
-
Torricellis Law states that water will flow from an opening at the bottom of a tank with the same speed that it would attain falling from the surface of the water to the opening. One of the forms of...
-
2. Modifying organizational structure to fit the communication needs of the organization
-
1. Clarifying and defining jobs
-
8. Can paperwork regarding this job be eliminated?
![Mobile App Logo](https://dsd5zvtm8ll6.cloudfront.net/includes/images/mobile/finalLogo.png)
Study smarter with the SolutionInn App