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Trig/Physics Question

Hi guys.

This question has a physics context but should be solved using trig:

An athlete runs around a perfectly circular track that has a radius of 80.0 meters. He runs at a constant speed of 1.50 meters per second, and runs for 5 minutes. What is his displacement (direct change in position, measured in a straight line)? Use the below diagram to help.

(Note: this was pretty much how the diagram I was given looked like; I’m assuming the dot represents his stopping point and 80 was where he started at; I’m not sure if the diagram my teacher gave me was drawn to proportion, so I didn’t dare use the scale on the axes to help me solve the question. Likewise, the dot I placed in this diagram might not be in the correct position, but the diagram was something like this.)

If anyone can help me solve this question, I’d be very thankful. :smile:

Here’s the diagram:
What have been your workings so far?

Do you know of a way you can determine the circumference of a circle given its radius? Can you see how this might relate to the problem?
you need 3 skillz

i) distance,speed, time

ii) relating the arc of a circle to the angle subtended

iii) SOHCAHTOA
Original post by the bear
you need 3 skillz

i) distance,speed, time

ii) relating the arc of a circle to the angle subtended

iii) SOHCAHTOA


I really don't think experimenting with foot worship is of any use in solving this problem...
Reply 4
Original post by Birkenhead
I really don't think experimenting with foot worship is of any use in solving this problem...


I have no contribution for the OP but I am not up to date with the latest language development so I just want to ask about "foot worship"
Original post by TeeEm
I have no contribution for the OP but I am not up to date with the latest language development so I just want to ask about "foot worship"


It was a fashionably bad joke.

SOHCAHTOA -> Suck her toe (in scouse)
Reply 6
Original post by Birkenhead
It was a fashionably bad joke.

SOHCAHTOA -> Suck her toe (in scouse)



I see...
That is all good since I also have no/bad sense of humour.

thanks
Original post by Birkenhead
I really don't think experimenting with foot worship is of any use in solving this problem...


i....i ... do i know you Sir ?
Reply 8
Original post by alex2100x
What have been your workings so far?

Do you know of a way you can determine the circumference of a circle given its radius? Can you see how this might relate to the problem?


The circumference was around 502, since 2π(80). The only use I had of it was to see whether his distance (450 = 1.5 ms^-1*5min) was the smaller arc or the larger arc. From there I used θ = ω/r to figure out the degree of the large arc in radians (5.625). Then I’m stuck.
(edited 9 years ago)
You know the distance of the circle around its circumference. You've stated this

You know how far he has ran. You've stated this too

You seem to understand that you need to find his point to some extent by finding the angle where he is to where he started.

Don't over complicate things by introducing radians. You really don't need to.
Original post by velocitous
The circumference was around 502, since 2π(80). The only use I had of it was to see whether his distance (450 = 1.5 ms^-1*5min) was the smaller arc or the larger arc. From there I used θ = ω/r to figure out the degree of the large arc in radians (5.625). Then I’m stuck.

If you have the angle as 5.625 radians, the end point must be in the bottom right quadrant since 3π2<5.625<2π\frac{3\pi}{2} < 5.625 < 2\pi. You can then draw a straight line from that point to the start to represent the displacement.

That line will form a chord to the circle since both of the points are on the circumference. You should also be able to find the minor angle subtended by the arc since you have the major angle as 5.625. Does this help?
Original post by Sam Walters
You know the distance of the circle around its circumference. You've stated this

You know how far he has ran. You've stated this too

You seem to understand that you need to find his point to some extent by finding the angle where he is to where he started.

Don't over complicate things by introducing radians. You really don't need to.

I'll be interested to see how you would go about doing this without using radians. The way I did it involved radians and a bit of circle theorems, but I can't see a way of doing it without.

It is late, though, so I'll have another look at it in the morning.
Original post by Malgorithm
I'll be interested to see how you would go about doing this without using radians. The way I did it involved radians and a bit of circle theorems, but I can't see a way of doing it without.

It is late, though, so I'll have another look at it in the morning.


You've given him how to do the rest of it. So ill just explain what I mean.

502.65482457436691815402294132472 m for the outside circumference. (I don't like rounding until final answer, just so you know)

Hes ran 450 m.

450/502.65482457436691815402294132472=0.89524655489191126369997116897039

Given that's a proportion of the circle hes ran around

0.89524655489191126369997116897039*360= 322.288759761088054931989620829 degree. so -37.7112402389119450680103791706

As a double check you can use θ = ω/r. (Always good to put little checks in!)

322.288759761088054931989620829=5.625 radians.

You've done the same thing. I'm just lazy. Id probably chop that angle down in two so i can deal with it as a right angled triangle too as like I said. I'm lazy and i have the hyp. Find the opp and double it up. Bish bash bosh.
(edited 9 years ago)
Original post by Sam Walters
You've given him how to do the rest of it. So ill just explain what I mean.

502.65482457436691815402294132472 m for the outside circumference. (I don't like rounding until final answer, just so you know)

Hes ran 450 m.

450/502.65482457436691815402294132472=0.89524655489191126369997116897039

Given that's a proportion of the circle hes ran around

0.89524655489191126369997116897039*360= 322.288759761088054931989620829 degree. so -37.7112402389119450680103791706

As a double check you can use θ = ω/r. (Always good to put little checks in!)

322.288759761088054931989620829=5.625 radians.

You've done the same thing. I'm just lazy. Id probably chop that angle down in two so i can deal with it as a right angled triangle too as like I said. I'm lazy and i have the hyp. Find the opp and double it up. Bish bash bosh.

That's essentially what I did, using the perpendicular bisector of the chord to find half the length of the chord, then doubling.
Original post by Malgorithm
That's essentially what I did, using the perpendicular bisector of the chord to find half the length of the chord, then doubling.


You could have done it by using cosine and all that jazz. But i try not to rearrange any equations if i can. I don't like to introduce places where there is potential to cock up.

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