Assignment 10

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course Mth 277

If your solution to stated problem does not match the given solution, you should self-critique per instructions athttp://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

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Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

qa 10_03

If the velocity function for a projectile is `v(t) = 10 `i + (20 - 9.8 t) `j, then:

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Question: `q001. What is its position function `R(t), and what is its acceleration function `a(t)?

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Your solution:

R(t)= 10ti +(20t-4.9t^2)j

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Integration has an arbitrary constant c_1 `i + c_2 `j, so the general solution would be

R(t)= (10 t+c_1)i +(20t-4.9t^2 + c_2)j

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A(t)= -9.8j

confidence rating #$&*:

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Given Solution:

Velocity is the derivative of position, so you need an antiderivative.

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Question:

`q002. What is its position function if its t = 0 position is `R(0) = 0 `i + 10 `j?

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Your solution:

R(t)= 10ti+ (20t-4.9t^2+10)j

confidence rating #$&*:

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Given Solution:

Your antiderivatives contain integration constants. From the given conditions you can evaluate those constants.

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Question:

`q003. At what instant is the `j component of the position function equal to 20?

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Your solution:

20=20t-4.9t^2+10 if t=3.49825 or 0.583382.

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Question:

`q004. At what instant is the `i component of the position equal to 20, and at that instant what is the `j component of its position?

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Your solution:

At t=2 the i component is 20 and the j component is 30.4

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Question:

`q005. At what instant is the `j component of its position maximized?

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Your solution:

-9.8, found by the second derivative.

confidence rating #$&*:

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Given Solution:

A function is maximized or minimized at a critical point. A first- or second-derivative test can check whether a critical point gives us a max or a min, or perhaps an inflection point.

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Question:

`q006. At what instant is the `j component of its position zero, and at that instant what is the `i component of its position?

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Your solution:

The j component is zero when t=4.53195 and the I component is 45.3195

confidence rating #$&*:

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Given Solution:

The quadratic formula might be useful.

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Question:

`q007. At what instant is the angle between `R(t) and the `i vector equal to 70 degrees? Does this occur at only one instant?

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Your solution:

Cos(theta)= (R(t) dot i)/ magnitude of R(t) times the magnitude of i= (<10t, 20t-4.9t^2> dot<10t>)/ sqrt(100t^2)*sqrt(100t^2+400t^2-196t^3+24.01t^4)

So, 70=cos^-1( 10/(t*sqrt(500-196t+24.01t^2))) then t must be about 2.25.

confidence rating #$&*:

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Given Solution:

Use the dot product to get an expression for the angle.

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Question:

`q008. Give a set of parametric equations x = x(t) and y = y(t) that describe the position of the projectile. Eliminate the variable t, and solve for y in terms of x. What kind of equation do you get? Describe its graph.

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Your solution:

If R(t)=10ti+(20t-4.9t^2+10j, then x=10t and y=20t-4.9t^2=10.

T=x/10

Y= 2x-0.049x^2+10, this is a parabola.

confidence rating #$&*:

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Given Solution:

The position is x(t) `i + y(t) `j. You figured out the position function in the second problem.

You eliminate the variable by solving for either x or y in terms of t, then substituting in the equation for y or x (depending on whether you solve the x or the y equation for t).

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Self-critique (if necessary):OK

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Self-critique rating:OK

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Very good work.

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