How much of a head start does B need to win the race?

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SUMMARY

In a race of 50 meters, runner A, traveling at 5 m/s, will win against runner B, who runs at 3 m/s. To determine the head start B needs to win, the equations of motion were analyzed. By setting the time taken for both runners to complete the race equal, it was concluded that B requires a minimum head start of 20 meters. The calculations yield that both runners would finish the race in 10 seconds.

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  • Knowledge of linear motion principles.
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NotASmurf
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Hey all. Simple problem here. 2 people are running at 2 different speeds in a race 50m long (A at 5 m/s B at 3 m/s), A is clearly going to win, How much of a head start would B need to win?
(This isn't a homework problem I'm just wondering how long I have to wait for my movie to buffer before I should start watching it.)
 
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Min 20 metres.
 
Min?? Working out?
 
Minimum of 20 metres.
 
let the headstart be denoted by' x' and time taken to complete the race be 't'. Note that time will be same for A and B. Now, using the fact that
Distance traveled = Speed* time, we have
For A, 50= 5*t
For B, 50=x + 3*t
Solve these to get x=20, t=10
 
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