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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.

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

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

Your solution:

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Given Solution:

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

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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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Given Solution:

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

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Question:

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

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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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Question:

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

Your solution:

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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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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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Given Solution:

The quadratic formula might be useful.

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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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Given Solution:

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

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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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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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