Grade 12 Motion Problem Question

[socialfox1]

Hi there everyone, I just finished this question but have no idea whether it is right or wrong. I have attached a picture of my work and so can anyone just look it over and see if it is correct please? I've uploaded the question sheet (focus on number 4 only) and my answer to number 4.

Thank you and have a blessed day!

 

[BvU]

Wonderful. Pick up the template and try again. Be meticulous.
And: we will try to help you. Please give us a chance.

 

[socialfox1]

Hi thanks for checking it over, any chance you can tell me where I went wrong so I can focus on that area please?

 

[BvU]

No, what I asked was: Pick up the template and try again. Be meticulous.

 

[socialfox1]

Okay, I assume you mean I had it wrong, I will try again then.

 

[BvU]

I can't for the life of me figure out if you had it right or wrong. Picking up the template means sorting out what is asked, what ammo you have to answer and what exactly you have done so far.

Homework Statement

Homework Equations

The Attempt at a Solution

PF rule is: you don't bother to help us help you, then you'll be last in line.

Please understand that from what you gave us so far it is excruciatingly difficult to understand what you are working on and where exactly you run into trouble.

And in spite of this severe response: welcome to PF. If we can, we will help.

 

[socialfox1]

Whoops, sorry about that first time here...

1. Problem:
The Gingerbread Man and the Pillsbury Dough Boy decides to settle their long standing differences on the track. Being very confident in his superior athleticism. The GBM decides to give the PDB a head start of 20m. The GBM achieves an instantaneous velocity of 10m/s. Dough boy knows he cannot beat the GBM fairly so he jumps into his Dough Mobile which accelerates at 2m/s^2. When will the GBM pass DB? What is DB's velocity when GBM passes DB? Which baked good will win the race if it is 80m long?

So for the variables, I have the following:
Gingerbread Man:
Delta V= 10m/s
Acceleration = 0

Pillsbury Dough Boy:
Delta Distance = 20m
Acceleration = 2 m/s^2
v1 = 0 m/s
v2 = ? Unknown

2. Homework Equations

Delta D= (v1)(delta t)+0.5(a)(delta t)^2
Delta D= (v2)(delta t)-0.5(a)(delta t)^2
a= (v2-v1)/t

3. Attempt at solutions
I've attached a picture.

I'll keep this template in mind from now on, sorry for not reading the rules.

 

[BvU]

Bravo ! Good story, pleasure to read.
Just a little more sorting out: ##\Delta D## now causes trouble. Until you're fluent with this, better use
##x(t)=x(0)+v_0\ t + {1 \over 2} a\ t^2##

For GBM this means ##x(t) = v_0\ t##

For PDB you have ##x(t) = {1 \over 2} a\ t^2##

For the thrilling moment of overtaking you have GBM x(t) = PDB x(t) from which you can extract t.

The the x(t) expressions tell you where that happens, which isn't explicitly asked for. But remember the value.

Your other relevant equation is ##v(t) = v_0 + a\ t## right ? The cheat PDB starts at velocity zero so with t known you know the second answer.

For the third answer you say one thing if the x value you noted down is less than 80, the other if it is more. If it is exactly 80, the race is a draw, but I don't expect that!

Good luck and if you catch up with them, bon appetit!

 

[haruspex]

I doubt you're supposed to be solving this using tables of speeds and distances after various times. That's prone to granularity errors. You need to develop the equations.
At time t, how far has GBM gone? At time t, far has PDB gone? What equation can you write to express that GBM catches up with PDB at time t?
(Best practice is to work entirely symbolically, only plugging in numbers at the final step. You need different symbols to represent the given numbers.)