A particle describe a central orbit ra = aa cos n under a force directed towards the pole. Find the law of Force.
(Rewrite the equation in terms of , take logarithms and differentiate with respect to
. Calculate
and use 3a) to find F.)
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State the type of modelling you will use for the given problem, giving reasons for your answers. Also state four essentials for the problem.
A company manufacturing soft drinks is thinking of expanding its plant capacity so as to meet future demand. The monthly sales for the past 5 years are available. To obtain good estimates for future demand so as to help the company make the right decisions.
A body of constant mass m is projected vertically upward with an initial velocity v0 in a medium offering a resistance k | v | , where k is a constant. Neglect changes in the gravitational force.
i) Find the maximum height xm attained by the body and the time tm at which this maximum height is reached.
ii) Show that if kv0 /mg < 1, then tm and xm can be expressed as
Use this to write down the equation of motion of a particle under a force F = cu3 , where c is a constant. Solve the equation of motion. You will need to discuss three cases c > h2 , c = h2 and c < h2 . Discuss, in which of these cases, is a closed orbit possible.
Find the current density when oxygen diffuses through a red cell of thickness 2.5 10-8 cm , the two ends of which are maintain at a fixed concentration C0 .
A particle is projected from the base of an inclined plane making an angle a with the horizontal. The initial velocity of projection is making an angle with the horizontal.
i) Derive the equation to the trajectory.
ii) Find the point at which the particle strikes the plane.
Suppose we find the sum of solutions obtained in (i) and (ii) of (b) above. Does this give a solution of the equation describing the motion? If yes, what physical situation, this solution will be correspond to? When is the velocity of the pendulum maximum? What type of energy does the pendulum have at position of maximum velocity?
Consider the pay-off table for two players given below
Player B
By graphical procedure determine the value of the game and the optimal mixed strategy foreach player.