Physics Question

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q1:4 ants start off at the corners of a square of side D. They start marching towards each other when the starter’s flag goes up. They move at a constant speed v, with their instantaneous motion always directed at the ant immediately facing them. What is the shape of the path taken?https://jasmcole.com/2014/07/15/ant-ics/ Do the ants meet at the center in finite time? *Please solve the question using r and theta and treat center as the origin point. If so, how long do they take? (These ant are point particles). *thus MUST create an integral and compute following the graph 1 for question and graph 2 as guide to solve the problem

q2: The chain of length l and mass m is held at the top such that it hangs vertically with its bottom end just above a weighing scale. So assume it can not be expanded, neglect the tension when it was pulled by the already fallen parts and set the density as m/l. It is then released. What is the reading on the scale as a function of the height of the top of the chain? Write the solution as a function of time and also Sketch the solution as a function of time.

q3:the particle of mass m slides down an inclined plane under the influence of gravity. The particle starts from rest, and is subject to a drag force. We consider two models for drag: F = – k*v and F = – k*v^2 . For both cases, please find the velocity v(t) and the time τ it takes to the particle to move a distance d. (In the case where the drag force is kv, you can assume that τ ≫ m/k to find an explicit expression for τ ). assume the angle is theta

q4:consider a particle with mass m and energy E > 0 moving in a one-dimensional potential V (x) = A*|x|^n , with A, n >0. Find the turning points of the motion. Find an explicit integral expression for the period of oscillation T as a function of A, n, m, and E. Check that you recover the expected result for simple harmonic motion when n = 2