Donald plays Monopoly and draws the "Go straight to jail" card. After an outburst of rage, Donald decides that he wants to go to prison as soon as possible, but discovers that there is a swamp between him and the prison. Donald is in point (2, 0) and the prison in (−2, 0) and the swamp is within the curve, |x| + |y| = 1. all targets in Duck City Units. Donald moves with a speed 1 outside the swamp and constant speed v> 0 in the swamp. What can the speed v in the swamp be if: (i) The fastest route involves starting by going straight to a point (a, b) at the edge of the swamp with 0 <| b | <1 (illustrated in the figure)? In that case, find b as a function of v and draw the graph (2sqr(b^2+(2-a)^2) + 2a/v we know this is the fastest rout, but why??
Donald plays Monopoly and draws the "Go straight to jail" card. After an outburst of rage, Donald decides that he wants to go to prison as soon as possible, but discovers that
there is a swamp between him and the prison. Donald is in point (2, 0) and
the prison in (−2, 0) and the swamp is within the curve, |x| + |y| = 1.
all targets in Duck City Units. Donald moves with a speed 1 outside the swamp and
constant speed v> 0 in the swamp.
What can the speed v in the swamp be if:
(i) The fastest route involves starting by going straight to a point (a, b) at the edge
of the swamp with 0 <| b | <1 (illustrated in the figure)? In that case, find b as a function of v and draw the graph
(2sqr(b^2+(2-a)^2) + 2a/v
we know this is the fastest rout, but why??
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