Is this homework question missing information?

[ksinelli]

Here is the problem word for word:

Isaaic and Blaise decide to race. They both start at the same position at the same time. Isaaic runs at 2 m/s but decides to take a 2 minute rest stop. Blaise runs at half the speed and still wins by 10 meters. How far did Blaise run?

I can use only these equations.

X = V_avgT

V_avg = (V_f - V_i)/T

A = (V_f - V_i)/T

V_f² = V_i² + 2ax

X = V_iT + (1/2)at

This is as far as I've gotten.

X_b = (1m/s)T_b

Blaise's distance is equal to his average velocity times his time.

Blaise's time is equal to Isaaic's time + 120 seconds

X_b = (1m/s)(T_i + 120s)

Blaise's distance is equal to Isaaic's distance + 10 meters

X_i + 10m = (1m/s)(T_i + 120s)

but now i have no idea what to do. Shouldn't they have given me the acceleration? If we assume the acceleration to be 0 and try to solve for T_i, you end up dividing by 0 which leads nowhere.

Am I just not seeing the solution or is this problem missing some information?

 

[jhae2.718]

We know that Blaise and Isaac run at constant speeds. Therefore, we can write their positions as a function of time. You've done this correctly for Blaise; you need to get an expression for Isaac's position.

Now, if you know that Blaise runs 10 m more than Isaac, how can you relate x_b and x_i, Blaise's and Isaac's final positions?

Set this as the final condition for Isaac's and Blaise's position functions (we'll call the time this happens at t_f). You now have two equations with two unknowns and can solve it algebraically.

 

[ksinelli]

We know that Blaise and Isaac run at constant speeds. Therefore, we can write their positions as a function of time. You've done this correctly for Blaise; you need to get an expression for Isaac's position.

Now, if you know that Blaise runs 10 m more than Isaac, how can you relate x_b and x_i, Blaise's and Isaac's final positions?

Set this as the final condition for Isaac's and Blaise's position functions (we'll call the time this happens at t_f). You now have two equations with two unknowns and can solve it algebraically.

ah! I remember now! Lol it's been so long since I've done this stuff, I'm actually trying to help my girlfriend with her physics homework. But I understand what you're saying and now I can explain it to her. The next step was so deceptively simple. Thanks :)

 

[ksinelli]

i'm not going to lie i feel really stupid. i thought i understood this but i replied prematurely.

i'm still stuck.

i've got both isaac's and blaise's position as a function of time with these equations

X_i = (1m/s)(T_i + 120s) - 10m

X_b = (2m/s)(T_b - 120s) + 10m

and as for how to relate their final positions... Blaise wins by 10 meters so...

X_b = X_i + 10m

says that blaise's position is equal to isaac's position + 10 meters

Then what I thought I was supposed to do was input the expressions for X_i and X_b to solve

2m/s(T_b - 120s) + 10m = 1m/s(T_i + 120s) - 10m + 10m

So the above says X_b = X_i + 10m and then i thought I could solve from there.

But I still have two variables and it seems the only thing I can do is relate T_b in terms of T_i or vice versa. Am I on the right track or did I go wrong somewhere? If I'm going in the right direction, what do I do next?

 

[jhae2.718]

Your function for Isaac's position is wrong. T_b=T_i+120, so Isaac's position function should just have T_i, not +/- 120 s. You also switched Blaise's and Isaac's velocities.

I'd recommend letting the initial position of both be zero. If Isaac's position function is x_i(t), then x_i(t_final)=x_if, some final position. By the question, then, Blaise's final position x_bf=x_if+10.

This occurs at some time t_final. We don't really care what it is for this question; we just need to rearrange one equation to equal t_final, which we then substitute into the other and solve for x_bf.

 

[ksinelli]

Your function for Isaac's position is wrong. T_b=T_i+120, so Isaac's position function should just have T_i, not +/- 120 s. You also switched Blaise's and Isaac's velocities.

I'd recommend letting the initial position of both be zero. If Isaac's position function is x_i(t), then x_i(t_final)=x_if, some final position. By the question, then, Blaise's final position x_bf=x_if+10.

This occurs at some time t_final. We don't really care what it is for this question; we just need to rearrange one equation to equal t_final, which we then substitute into the other and solve for x_bf.

I finally came back to this problem a month and a half later after giving up. I spent about two hours dissecting your posts, reading them over and over to try to fully understand the help you were giving. I did manage to solve the problem and I realized a few things.

My equations were not wrong. You just did not take the time to fully read and understand them. Also, you made a mistake by saying Isaac's position function is X_i(t). I think what you meant to say was his position is determined by his velocity multiplied by his time, not that his position is determined by his position multiplied by time.

My problem was that I didn't understand the math required to isolate T_i on one side of the equation in order to solve for it. Unbelievably simple, I know, but I haven't done algebra in over 7 years.

I appreciate that you are willing to help, but please take the time to understand what people have written and to make sure that what you have written is correct. It's very frustrating to be pointed in the wrong direction and I'm a bit disheartened that no one else bothered to help.