Homework Help: Constant velocity Problem

1. Nov 4, 2008

scottzilla

1. The problem statement, all variables and given/known data

Speedy tortoise can run 10cm/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2 minutes. The tortoise wins the race by a shell (20cm). A)How long does the race take? B)What is the length of the race.

2. Relevant equations

3. The attempt at a solution
For some reason I am lost on how to set up this problem. I keep wanting to use motion in 1 dimension with constant acceleration but I cannot come up with the answers given in the book. A step by step explanationj on how to solve this type of question would be awesome.

Scottzilla

2. Nov 4, 2008

Hootenanny

Staff Emeritus
This question is probably a little simpler than you're trying to make it.

Okay, let's start by writing down what we know. Suppose that the length of the track is L and the time taken for the tortoise to complete that race, T, such that

$$v = \frac{dx}{dt}\Rightarrow 10 = \frac{L}{T}$$

Next we have the hare's information. We know that the hare stops of 2 minutes or 120 seconds, so the total time the hare is running is T-120. We also know that when the tortoise is at the finish line (x=L), the hare is 20cm behind him, i.e. x=L-20. Finally, we know that the hare can run at 20x10 cm/s. Hence,

$$v = \frac{dx}{dt}\Rightarrow 200 = \frac{L-20}{T-120}$$

Do you follow?

3. Nov 4, 2008

scottzilla

Ok I think I follow you. When I was trying to come up with my equations I was taking the hare's distance to be equal to the tortoise's distance minus 20cm. SO should I take those equations and solve one for (T)ime and then put that equation into the other one?

4. Nov 5, 2008

Hootenanny

Staff Emeritus
That's exactly what I've done with my set of equations, L-20
Sounds good to me