Maths

[pahee]

It will be a great help if somebody can help answering the (c) part of this question, which appeared in the CSSE 11+ examination for 2017 entry Question no 15.

Jo ties a rope from a branch of a tree overhanging a river. She stands on the bank holding the rope and then launches herself to swing out over the river and back to the bank where she stops.
The graph shows her distance from the bank at different times from the start.



Note: the following is the data extracted from the graph, which does not shown in the question.

Time in Seconds after start Distance from the bank in meters

0 0
0.5 1
1 3
1.5 4
2 3
2.5 1
3 0

there is a graph drawn in the question time in the X axis against distance in the Y axis, you can view the graph by clicking on the URL link below.

https://www.flickr.com/photos/11040888@N03/?

(a) How far does jo travel in total? Answer: 8 Meters

(b) For how long is Jo more than 3 meters from the bank? Answer: 1 Second

(c) How far from the bank is she when she is travelling fastest?

[RomfordDad]

Strictly speaking, you can't answer the question if they don't provide a function, as one should calculate a derivative.

You need to look at the point where the line is steepest (either increasing or decreasing fastest), at that point(s) Jo covers largest distance in a given period of time (speed = distance/time = distance on y axis / distance on x axis). From the graph, it looks like 2m from the bank, Jo's speed is increasing gradually up to 2m from the bank, then she's slowing from that point to reach 4m where Jo is still, then Jo speeds up again to reach max speed at 6m (being 2m from the bank again) and slowing down from there.

[Guest55]

RomfordDad you can find it by looking at the gradient of the tangent or judging by eye - personally I do not think this is an appropriate question for 11+.

[pahee]

Thank you RomfordDad and Guest55 for your comments, it was a question in the CSSE 11+ Examination last year, and it is only a D/T (Distance against Time) graph and for 11+ children I believe that the examiners cannot expect the candidates to understand the equations of graphs. I too agree this is not an accurate question in the sense, there is no mentioning in the question about where exactly Joe tied the rope in the branch of the tree over hanging the river. If it is straight above the place she is standing or bit away from the bank towards the middle of the river.If it is straight above the place she is standing she will be performing only one half of the oscillation (or swing) before returning to the place where she was standing. She will be standing at the middle point of the swing and where the speed will be the highest. if she managed to tie the rope further away towards the river she will be performing more than half of the oscillation and the point she will be standing may not be end of the oscillation where the speed may not be zero.

[ToadMum]

CSSE papers normally come with the marking scheme. What was the answer given?

[Guest55]

The speed is lowest in the 'middle' of the graph as she stops and starts to come back.

[ToadMum]

Just looking at it, would the answer to c) be 'between 1 and 3 metres'?

Jo travels one metre in the first half second, but two in the next half second - and then on the way back, she travels from 3 metres away to 1 metre away in half a second, then takes the same time to travel the last metre.

Would still like to know what it says in the marking scheme...

[nyr]

I reckon it's a mistake and they meant slowest rather than fastest.

[Catseye]

The graph is wrong !
it would look more like inverted 'wavy' V with very short period of constant velocity, ie acceleration = zero i.e natural rest point given the forces of friction and air resistance.

So, you are all are wrong , the examiner has no idea of SHM which is a smooth sine wave in perpetual motion which physics forbids as per the the Laws of Thermodynamics/ Conservation of momentum.

As you were were.

You can say want ever you like but if you contravene the Laws of thermodynamics or the conservation of momentum then you know you are wrong !!

[Guest55]

SHM would not be a 'perfect description' as rope is not 'light' and the tying [ie the attachment] of the rope would bring in external forces.

However, I agree that the question is poor ..