Car chase: will the cars meet?

[ujellytek]

Homework Statement

There is a speedy car chase! A thief is getting away from a police officer. The distance between them at the start is 100m. The thief starts to accelerate at 5.0m/s^2 [F] from rest. Meanwhile the police is chasing him at its max velocity of 30m/s (sad... I know XD). Show that the police officer NEVER CATCHES UP to the thief.

Please take a gander at section 3 and answer this:

i) First off, is my solution correct?

ii) Ok... this seems to be the correct solution because they are NOT supposed to meet-up/collide during the car chase at all, because subbing in 6s into both equations gives 90m and 80m, but how can the quad formula say that at 6s they do meet (why do we get this mathematical inconsistency?)?

iii)Or did I just do It wrong? Please explain this in more depth if you want, or just show me how to solve it, this is kind of a bonus question and I need ALL the marks I can to get into software engineering, please help!

~Thanks

P.S. I will watch this thread inthe next little while, and in 10 hours plus a constant span of 75min (my period 1 spare) [i'm also interested in question 2)ii) quite a bit].

Homework Equations

The Attempt at a Solution

So since the officer stars 100 meters behind I got: d=t*30-100
and for the thief I got: d= v*t+0.5*a*t^2 which becomes d=2.5*t^2 because thief starts at rest

Then I make these two equations equal to each other: t*30-100=2.5*t^2 and I make it equal to 0;
thus 0=2.5*t^2-30t+100 and when I apply the quadratics formula I get i2 seconds and 6 seconds.

Now when I sub 2s into the officers displacement equation I get: d(6s)=(6)*30-100= 80m
and, for the thief I get: d(6s)=2.5(6)^2= 90m

I get a mathematical inconsistency and that satisfies the question.

 

[gneill]

I think you need to check your quadratic equation again. What did you get for the discriminant?

 

[ujellytek]

I think you need to check your quadratic equation again. What did you get for the discriminant?

Ohh, I'm using a SHARP calculator that can use Quad formula by plugging in A,B,C of quadratic equation (it's never given me a wrong answer before), when I plug in 2.5 -30 and 100 I get i2 and what appears to be 6 (my screen is broken, but I can assure you it is a 6). When I Try my own quad formula I get the discriminant of (-100) -> (B)^2 - 4(A)(C) right? (-30)^2 -4(2.5)(100) = 900-1000 = -100

Any ideas why my calc is giving me a real integer?

 

[gneill]

Ohh, I'm using a SHARP calculator that can use Quad formula by plugging in A,B,C of quadratic equation (it's never given me a wrong answer before), when I plug in 2.5 -30 and 100 I get i2 and what appears to be 6 (my screen is broken, but I can assure you it is a 6). When I Try my own quad formula I get the discriminant of (-100) -> (B)^2 - 4(A)(C) right? (-30)^2 -4(2.5)(100) = 900-1000 = -100

Right. What does it mean when the discriminant is negative?

Any ideas why my calc is giving me a real integer?

Yes, it didn't It gave you one complex result: (6 + 2i), not 6 and 2i. There's probably another root accessible through some manipulation of the calculator's registers.

 

[ujellytek]

Right. What does it mean when the discriminant is negative?

Yes, it didn't It gave you one complex result: (6 + 2i), not 6 and 2i. There's probably another root accessible through some manipulation of the calculator's registers.

Ahh, that makes a lot of sense, my calc shows X1=6, which is probably 6+ some bugged value, and X2=i2 which is probably 6(which is bugged out) +i2, thanks a lot!