Solving an Inconceivable Problem: Comparing Methods for Calculating Vc

[vebes02]

Homework Statement

To set a speed record in measured (straight) distance d, a race car must be driven first in one direction (in time t1) and then in the opposite direction (in time t2). (a) To eliminate the effects of the wind and obtain the car's speed vc in a windless situation, should we find the average of d/t1 and d/t2 (method 1) or should we divide d by the average of t1 and t2? (b) What is the fractional difference in the two methods when a steady wind blows along the car's route and the ratio of the wind speed vw to the car's speed vc is 0.0240?


2. The attempt at a solution
I've tried Part A, and got:
Method 1: Vc = 1/2[d/t1 + d/t2]
Method 2: Vc = 2d/(t1 + t2)


Overall, this problem is irksome. I've spent the past 2 hours working on it, and my answers have become inconceivable. It's not even one of the problems I'm assigned to do, but I have an annoying tendency to finish whatever I completed, meaning if I wrote the problem down, I have to solve it.

So to those who can help, much appreciation.

 

[CompuChip]

Welcome to PF.
Actually (as is not uncommon in physics), the physics of this problem is really easy, it's just the algebra that may give you headaches. You can just use the formula d = v t, where v is the effective velocity and t is the time. You can write down expressions for v = v1 when t = t1 and for v = v2 when t = t2. This gives you two equations: use one of them to eliminate vw (the speed of the wind) and you will get an equation for d in terms of vc, t1 and t2 from which you can obtain an equation for vc in terms of d, t1 and t2.

 

[vebes02]

What I'm not sure about is, is d the total distance covered, or merely the distance traveled in one direction?

 

[Redbelly98]

d is the distance in 1 direction.

 

[vebes02]

But if we get rid of vw, how would we be able to incorporate 0.0240 into the problem?

 

[Redbelly98]

It seems we have not been given the information required. How is the car's speed affected by the wind speed vw? Is there a discussion of this in your textbook somewhere, or is there more info given in the problem statement that was not included in your original post?