Analyse the motion of a jogger
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Analyse the motion of a jogger

[From: ] [author: ] [Date: 11-09-11] [Hit: ]
highlight the two cells and then move the mouse to the lower right hand corner of A3. A black cross should appear; click and hold this area and drag it down until you see the numbers count to 7.6. Make the next column for v; type =7.5*(1-0.04*A2)^(0.......
Based on observations, the speed of a jogger can be approximatedby the relation v=7.5(1-0.04x)^(0.3), where v and x are expressedin mi/h and miles, respectively. Knowing that x=0 at t=0,determine (a) the distance the jogger has run when t=1h, (b)the joggers's acceleration in ft/s^s at t=0, (c) the time required for the jogger to run 6 mi.

Any help would be appreciated, thanks =)

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This is a question that should probably be handled with excel or some type of programming.
If you know how to use microsoft excel then you can try this method. The equation for v is given in the problem in terms of distance (x). Make a column for x starting at 0 and make a step of about 0.1. To do this type 0 into A2 and 0.1 into A3, highlight the two cells and then move the mouse to the lower right hand corner of A3. A black cross should appear; click and hold this area and drag it down until you see the numbers count to 7.6. Make the next column for v; type =7.5*(1-0.04*A2)^(0.3) into B2 and press enter. Highlight B2 and move the mouse to the lower right hand corner, this time don't drag it; just double click. This will copy the formula to the other cells in the B column. We'll use this data to create a step for time data. Remember that v*t=x so x/t=v. If we do this at a small step (in our case x=0.1, then we should be able to approximate time. In C3 type in =0.1/B3, copy this formula down to C78 by double clicking the cross at the lower right hand corner of C3. This is our data for a time STEP only. To find the actual time we'll have to progressively add these. In D2 type a 0, since x=0 when t=0. In D3 type =D2+C3, copy this formula down to D78 using the same trick mentioned early.

Summary:

Column A is for distance (type x into A1)
Column B is for velocity (type v into B1)
Column C is for the time step
Column D is for time (type t into D1)
use the data to answer the questions

a. The jogger has run about 7.2miles at t=1hours
b. Find the at t=0 using approximation with x=0 and x=0.1; the slope between the two is roughly:
-0.68(mi/hr)/s
c. The time required for the jogger to run 6 miles is roughly 0.83 hours or about 50 minutes.

This method is approximate but I hope it helps you out. If you graph these functions using excel you'll see that they're all just about linear.

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Sorry I was focused on analyzing the motions of a female jogger
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