Trying to tie two runners of different speeds over a race

[josephn]

Homework Statement

You can run 9.2 m/s , 20% faster than your brother. How much head start should you give him in order to have a tie race over 60 m ?

Relevant Equations

SUVAT

Attempt is attached, thanks for the help :)

 

[kuruman]

Thank you for your attempt. Is there a question you wish to ask?

 

[haruspex]

Error in first line: What is 20% faster than 7.36m/s?

 

[josephn]

9.2m/s?

 

[josephn]

Thank you for your attempt. Is there a question you wish to ask?

not sure where i went wrong as the answer is incorrect

 

[kuruman]

You have a race between a fast and a slow runner. The idea is to make the race fair by giving the slow runner a head start. To me this means starting the runners at the same time but with the slower runner closer to the finish line. How much closer in meters is the question to answer.

 

[haruspex]

9.2m/s?

What is 20% of 7.36? What do you get if you add that to 7.36?

 

[PeroK]

Homework Statement: You can run 9.2 m/s , 20% faster than your brother. How much head start should you give him in order to have a tie race over 60 m ?

It can't matter how fast you and your brother can run. The only thing that matters is that you can run 20% faster than him, which means you run 20% further in a given time.

PS I was assuming "head start" meant distance. That's the way it's done in athletics in a handicap race.

If "head start" means time, then that is a different matter.

 

[pbuk]

To me this means starting the runners at the same time but with the slower runner closer to the finish line.
How much closer in meters is the question to answer.

From the context of the question (and from general knowledge of how head starts work in races) this is not the case. How much earlier in seconds is the question to answer.

It can't matter how fast you and your brother can run.

Yes it can, and does.

The only thing that matters is that you can run 20% faster than him, which means you run 20% further in a given time.

But there is no 'given time': there is a given distance, 60 metres. The only thing that matters is the difference in time for each athlete to run that distance.

@haruspex hit the nail on the head in post #3.

 

[PeroK]

Yes it can, and does.

I was assuming "head start" meant distance. There used to be a handicap sprint event in Edinburgh (on New Year's Day, I think). The top competitors would run 110m, and the others would start further along the track depending on their age and/or ability.

https://en.wikipedia.org/wiki/New_Year_Sprint

 

[kuruman]

From the context of the question (and from general knowledge of how head starts work in races) this is not the case.

I am not so sure. In oval tracks the runner on the outside has to cover a longer distance than the runner on the very inside, which is unfair if they all started at the same time. For the 200 m race for example, runners start on the curved section at the track and run towards the opposite curved section. As the outer lanes are longer than the inner lanes, a staggered start is needed so that, at the finish line, all runners have run the same distance. From a practical point of view, it would be a logistical nightmare to start several eager-to-go runners at equally spaced time intervals.

Of course here we have a straight 60-m distance and only two runners. Nevertheless, the statement of the problem could have been clearer by specifying whether the expected "head start" has units of distance or time.

On edit:
I crossed out an infelicity. A 200 m dash is 200 m for all runners who have to cover the same distance. The purpose of the race is to see who gets to the finish line in the shortest time.

 

[gmax137]

In drag racing, the headstart is in time. The slower car gets the green light first.

 

[gmax137]

@haruspex hit the nail on the head in post #3

Yes. 9.2 x 0.8 is not the same as 9.2 ÷ 1.2.

This is a key source of confusion in problems framed using percentages.

 

[pbuk]

In drag racing, the headstart is in time. The slower car gets the green light first.

In almost all racing head starts are in time. A head start in terms of distance would only work fairly if all competitors accelerate in zero time to a speed which remains constant for the rest of the race, which is clearly impossible, or if each competitors speed profile over any possible distance was accurately modelled, which is clearly impractical.

 

[PeroK]

In almost all racing head starts are in time.

Wrong!

https://en.wikipedia.org/wiki/Head_start_(positioning)

 

[PeroK]

In almost all racing head starts are in time.

A good example is Formula One pole position. The advantage is distance, with all cars starting at the same time from different positions on the starting grid.

A head start in terms of distance would only work fairly if all competitors accelerate in zero time to a speed which remains constant for the rest of the race, which is clearly impossible, or if each competitors speed profile over any possible distance was accurately modelled, which is clearly impractical.

Trying to start a Formula One race with an advantage based on time from qualifying would be impractical.

 

[pbuk]

A good example is Formula One pole position. The advantage is distance, with all cars starting at the same time from different positions on the starting grid.

[Edited]I don't think that is a good example of a head start. The cars have to start in some order because the track is not 40 cars wide.

 

[PeroK]

No, that is not an example of a head start. The cars have to start in some order because the track is not 40 cars wide, and that order is determined by qualifying, giving an advantage to the fastest competitors. This is exactly the opposite of the purpose of a head start, which is to give a disadvantage to the fastest competitors.

So, if the slowest cars went first, then that would be a head start?

 

[pbuk]

Wrong!

https://en.wikipedia.org/wiki/Head_start_(positioning)

I don't know why you think that article indicates that I am wrong: the only example of a racing head start it gives is the modern pentathlon where the head start in the final race is measured in time, not distance.

@gmax137 has given the example of drag racing: again time not distance.

Other examples of time-based head starts include skiing (Olympic biathlon, Nordic Opening), combined winter sports (competitions using the Gunderson Method), and pursuit racing in sailing.

Apart from greyhound racing I cannot think of any widely-used distance-based head starts.

 

[pbuk]

But we have strayed widely off-topic: if you want a discussion about either the theory or practice of adjusting race times or distances according to performance this should be elsewhere.

 

[berkeman]

Thread is paused for Moderation...

 

[berkeman]

Thread is reopened provisionally. Please keep the side discussion about what a "head start" means in the new thread by @PeroK in the GD forum: https://www.physicsforums.com/threads/what-the-heck-is-a-head-start.1065266/

Thanks.

 

[josephn]

all i wanted was some help not a full on argument about it lol

 

[haruspex]

all i wanted was some help not a full on argument about it lol

Of course. Sorry about that - it happens.
Please see post #7.

 

[erobz]

all i wanted was some help not a full on argument about it lol

Sometimes we get hung up on the specifics or lack thereof. Like when I first wrote “there of”, and changed it after looking it up. I figured someone would say something about it…most people don’t care about things like that, but if you get corrected enough you too can have PTSD about what is correct!

 

[PeroK]

all i wanted was some help not a full on argument about it lol

Yes, but as a student of maths/physics it pays to be interested in the real world and how things work: times, distances etc. Here are my observations:

1) 9.2 m/s is really fast. It's elite level sprinting. (That's faster than I can cycle.) But, it is possible. I always check the numbers in questions to see whether the question setter knows anything!

2) Most races are from a standing start - so it's not enough to use only a sprinter's top speed. The question is lazy, IMO.

3) It's difficult to measure a sprinter's actual speed. All athletics is done on timings. What you would know is how fast (in terms of total time) you and your brother could sprint 60m on average (from a standing start).

4) 100 is not 20% more than 80. It's 25% more than 80. If you are 25% faster than you're brother then he's 20% slower than you. Percentages are tricky like that. Note that, for example, if the stock market goes up 50% one year and down 50% the other year, then it ends up having lost 25% over the two-year period.

 

[josephn]

What is 20% of 7.36? What do you get if you add that to 7.36?

isnt it just 9.2m/s?

 

[PeroK]

isnt it just 9.2m/s?

My calculator says no!

 

[gmax137]

9.2 x 0.8 is not the same as 9.2 ÷ 1.2.

This is a key source of confusion in problems framed using percentages.

4) 100 is not 20% more than 80. It's 25% more than 80. If you are 25% faster than you're brother then he's 20% slower than you. Percentages are tricky like that. Note that, for example, if the stock market goes up 50% one year and down 50% the other year, then it ends up having lost 25% over the two-year period.

isnt it just 9.2m/s?

I think we have zeroed in on the issue. EDIT @haruspex pointed this out in post #3.

Homework Statement: You can run 9.2 m/s , 20% faster than your brother.

Write that out as an equation:
$V_{you}=9.2 = 1.2 V_{bro}$
then $V_{bro} = \frac {V_{you}} {1.2}$

 

[SammyS]

isnt it just 9.2m/s?

@haruspex is asking you do do the calculation to check you result of 7.36 m/s for your brother's speed.

What is 20% of 7.36 ?

Take that result and add it to 7.36 .

What do you get?

It's not 9.2. is it ?

 

[Lnewqban]

9.2 m/s?

all i wanted was some help not a full on argument about it lol