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Mathematica (for Calculus I) Help?

Hello everyone!

I was given an optional Mathematica assignment (15 problems) that I am trying to work through. I was able to do all 15 except this gigantic, multi-step problem. Please see the question and then my code below. Thanks so much for your help!

Matt

  1. Suppose a ball is thrown upward and its position (in feet) above the ground after t seconds is given by the equation, s(t) = -5t2 + 150t + 25.

(a) Find the velocity function.

(Know how to do this one. ANSWER: 25 + 150t - 5t^2)

(b) How high is the ball at time t = 0?

s (t) = -5 t^2 + 150 t + 25

s (0) = -5 t^2 + 150 t + 25

ANSWER: 25

I can't seem to get the coding right for the next ones. They come up with error messages (even though I really thought I had C through I's coding done correctly!) :

(c) What is the velocity of the ball when the ball is at it highest point above the ground?

(d) What is the maximum height the ball will be above the ground?

(e) When is the velocity positive? What is the physical signi cance of this?

(f) When is the velocity negative? What is the physical signi cance of this?

(g) What is the velocity of the ball on its way up when its height is 600 ft?

(h) What is the velocity of the ball on its way down when its height is 600 ft?

(i) When (if ever) is the velocity 50 ft/sec?

(j) When (if ever) is the velocity 600 ft/sec?

(k) Find the total distance traveled by the ball from time 0 to when it hits the ground. Explain how you found this.

POSTED BY: Matt Ryan
3 Replies

Following up on David's excellent suggestion,

If you are given the position function, think about what the velocity function should be. They are not the same.

POSTED BY: Bruce Miller

WellÂ… I hope you can answer question (c) without doing any calculations whatsoever.

And, although you say that this was posed as a Mathematica problem, basically all of it can be done very quickly with a pen and paper and no digital help at all.

As much as I love and promote Mathematica, the greatest insight sometimes is gained by simply doing a calculation by hand. Using Mathematica for this problem is kind of like using high explosives to open up a jar of pickles.

And this sort of highlights some of the aspects of the debate around the question of using computer-based mathematics in place of hand calculations. Sometimes the focus on writing the computer code can divert one from pointing one's focus at gaining physical insight. So, take this just as a reminder that you should think about the physics first, whether or not you are doing your calculations by hand or with the help of a tool like Mathematica.

POSTED BY: David Reiss
Posted 10 years ago

Hi Matt, here is the definition of function s

s[t_] := -5 t^2 + 150 t + 25;

The value of s(0) can be obtained as follows

s[0]

for subparagraph (c), we derive with respect to t the function s in the following way

D[s[t], t]

Subsequently resolvermos s' = 0 with the help of solve

Solve[150 - 10 t == 0, t]

and as you can see on your graph of the function s, the maximum height is reached within 15 seconds, verify it with the command plot

Plot[s[t], {t, 0, 30}]

I hope that my help serve you so that you may resolve the following exercises,

POSTED BY: Luis Ledesma
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