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 =)
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.
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