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Lets look at this standard high school question. A football is kicked at ground level into the air at an angle of 30 deg to the horizontal. The speed at take off is 10 m/s. Find the time when it hits the ground. If you try this question, please list all the assumptions that you have to make.

To illustrate the point further, consider the following two systems: In the second case the mass of the rope is insignificant in comparison with the two masses at its ends. Whether you include it or not will not have a significant effect on the tension in the rope. This is the reason for...

This is a question about the application of Newton's laws which are taught in science to years 9/10 students, 11 and 12. A question that one has never seen in exams or texts does not mean the question is not legitimate and will not be asked in the future. Questions that require one to assume...

This question is not about density. See the original question.

Of course the rope is accelerating because the net force is not zero.

Did you mean major axis length 10 etc. y axis is the major axis? ok describe fully the locus of |z+5| - |z-5| = 8.

In my opinion the answer is 15 N at the end with the 15 N pulling force and 20 N at the other end. In the middle the tension is 17.5 N. You were right in saying the tension in the rope will actually vary throughout the rope but wrong (my opinion) to say the maximum tension is 15 N. To get the...

Not 30 N.

Ok Let say the rope has a uniform density and it lies on a frictionless horizontal surface. These were the unspecified assumptions when the question was posted. 15 N is not the answer. It can be answered using Newton's laws.

|x+i(y+1)|=\sqrt{x^2-i^2(y+1)^2}=\sqrt{x^2+(y+1)^2}

good answer, I'll let others to figure out why not.

I don't think \\|x+i(y+1)|=\sqrt{x^2-(y+1)^2} Also what shape is it?

Now pass on to you Is there a cartesian equation for |z + i| + |z - i| = 1?

If the rhs = 0 and the the lhs can be factorised. E.g. (x+y)(x-y)(y-x^2+3)=0

so what is the tension?

Try to sketch these (x+y)(x-y)=0 (x+y)(x+2y)=0 (x-y)(x^2+y)=0

A long rope is pulled with a force of 20 N at one end and 15 N at the other end. Is this possible and what can you say about the tension in the rope?

It is necessary because dy/dx is indeterminable at (0,0).

\large y=\begin{cases} \left ( \frac{3\pm \sqrt{5}}{2} \right )x & \text{ if } x\neq 0 \\ 0 & \text{ if } x=0 \end{cases}

I think \large y=\left ( \frac{3\pm \sqrt{5}}{2} \right )x So the graph is two lines. (0,0) is the intersecting point because it satisfies the original equation \large x^{2}-3xy+y^{2}=0 .