How long will it take Michael to catch Robert in a long distance race?

[bcaie16]

Homework Statement

In a long distance race, Michael is running at 3.8 m/s and is 75 m behind Robert, who is running at a constant velocity of 4.2 m/s. If Michael accelerates at 0.15 m/s^2, how long will it take him to catch Robert

Homework Equations

D=vi(delta)t + 1/2a(delta)t^2
etc

The Attempt at a Solution

I know how to do this type of problem when the accelerating runner starts from a rest, but I have no idea where to go from here. I've tried framing the problem a bunch of different ways but nothing.

 

[tiny-tim]

welcome to pf!

hi bcaie16! welcome to pf!

(have a delta: ∆ and try using the X² and X₂ icons just above the Reply box )

you need to write two separate equations, one for each runner …

what do you get? ​

 

[Delphi51]

Welcome to PF, bcaie16! Nice to see some high school work here.
The thing that determines the answer is that the two people meet - their distances become equal. So you should begin with
Michael's distance = Robert's distance

Robert's distance is easy - just use d = vt and add 75 because he is starting out that far ahead.

Michael's distance is complicated because of the initial velocity and acceleration. Use the standard distance formula for accelerated motion: d = Vi*t + .5*a*t².

It looks like you will have a quadratic equation to solve. If you are just starting grade 11 math you may need to look up how to solve a quadratic on a calculator or using the general formula:
http://en.wikipedia.org/wiki/Quadratic_equation

You can, of course, solve it by trial and error. A spreadsheet works really well for that.

 

[bcaie16]

I figured I would have to use the quadratic formula. I wasn't sure how to frame it kinematics wise. What are the a, b, and c values respectively in terms of velocity, acceleration, etc.

 

[bcaie16]

Ok i figured that the respective equations would be ∆t= 4.2 ∆D +75, and
75= -∆t +/- square root ∆t -2.28/2

 

[tiny-tim]

Ok i figured that the respective equations would be ∆t= 4.2 ∆D +75, and
75= -∆t +/- square root ∆t -2.28/2

nooo

(btw, why are you using all these ∆s? it's not normal, and it really doesn't help)

∆t= 4.2 ∆D +75 is completely wrong, isn't it?

and i can't work out what your second equation is

just write two general equations, one for each runner (ignoring the other) …

when you have them, then you can decide how to use them​

 

[bcaie16]

Ok being completely new to physics, I am kind of lost. I am not really sure to how to get a general equation. Should they be in relation to time or distance

 

[tiny-tim]

both …

each should be x = a function of t

(ie it tells you where it is at each time t )

 

[Delphi51]

Michael's distance = Robert's distance
vt + .5*a*t² = vt + 75
3.8*t + .5*(.15)*t² = 4.25 + 75
collect like terms, all on one side, so you have an equation of the form
at² + bt + c = 0
Then use one of the methods of solving the quadratic for t.

 

[Delphi51]

Oops, forgot a t in the previous post. Too late to edit. Should be like this:
Michael's distance = Robert's distance
vt + .5*a*t² = vt + 75
3.8*t + .5*(.15)*t² = 4.2t + 75
collect like terms, all on one side, so you have an equation of the form
at² + bt + c = 0
Then use one of the methods of solving the quadratic for t.