What is the speed of a speed skater at the finish line of a downhill course?

AI Thread Summary
A speed skater starts a 200m downhill course at 30 m/s and accelerates uniformly for 5 seconds. The calculation shows that her speed at the finish line should be 50 m/s, based on the equations of motion. However, the provided answer in the textbook is 45 m/s, which the participants in the discussion find incorrect. They agree that the average speed calculation does not support the textbook answer, leading to confusion about the accuracy of the published solution. The consensus is to address this discrepancy with the physics teacher upon returning to school.
jaxreid
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Homework Statement


A speed skater crosses the start line of a straight 200m downhiull course with speed of 30m per second. She accellerated uniformly all the way down taking 5 sec to cover the course - what is her speed at the finish line? I know this should be simple, but just can't get the answer to work out the same as the solution in the paper.


Homework Equations



s = 1/2 (u+v)t

The Attempt at a Solution


200 = 1/2 (30+v)5
200/5 = 1/2(30+v)
40 = 1/2(30+v)
2 x 40 = 30 + v
80 - 30 = v
v = 50m per sec

Answer in book is 45 - HOW?
 
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I have to wonder about the answer you are given. According to them the average speed is .5(30+45)=37.5 m/s. That won't cover the 200 m in 5 seconds. I agree with you.

The constant (uniform) acceleration rate is 4 m/s*s gotten from: x = V0*t+.5*a*t^2

Inserting that into Vf = V0 + a*t yields Vf=50 m/s.

So I don't understand either.
 
Lawrence - many thanks - was starting to think I'd lost the plot, am glad you agree. The question's from a past paper and the published answer was 45. Just goes to show, they don't always get it right, will point this out to my physics teacher when school returns on Tuesday. Thanks again for your prompt reply.

Jax
 
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