Donald plays monopoly and get "go direct to prison". He wants to go to the prison as fast as possible, but discovers there is a swamp between him and the prison. Donald is in the point (2, 0) and the prison (-2, 0), and the swamp inside the curve IxI + IyI = 1. Donald moves with a speed 1 outside the swamp, and constant speed v>0 in the swamp. What can the speed in the swamp be if: (i) The fastest way involves to start by going straight forward to a point (a, b) at the edge of the swamp with 0 < IbI < 1(se picture) if so , fin b as a function of v and draw the graph. (ii) the fastest way is to go outside the swamp (b= +- 1)? (iii) The fastest way is to go straight through the swamp (b= 0)? The task: Explain that the picture shows donalds path in case (i) and the time he uses can be given as a function of b t(b) = 2 *√(1+2b+2b2) +2 *((1-b)/v)
Donald plays monopoly and get "go direct to prison". He wants to go to the prison as fast as possible, but discovers there is a swamp between him and the prison. Donald is in the point (2, 0) and the prison (-2, 0), and the swamp inside the curve IxI + IyI = 1. Donald moves with a speed 1 outside the swamp, and constant speed v>0 in the swamp.
What can the speed in the swamp be if:
(i) The fastest way involves to start by going straight forward to a point (a, b) at the edge of the swamp with 0 < IbI < 1(se picture) if so , fin b as a function of v and draw the graph.
(ii) the fastest way is to go outside the swamp (b= +- 1)?
(iii) The fastest way is to go straight through the swamp (b= 0)?
The task: Explain that the picture shows donalds path in case (i) and the time he uses can be given as a function of b
t(b) = 2 *√(1+2b+2b2) +2 *((1-b)/v)
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