Suppose a lake is modelled by the region y- x > 0 in the plane. The shore is the straight line y - x = 0. Suppose a boat travels on the lake with position vector p(t) = tî + (1+ t²)ĵ at time t > 0. (a) Find the parallel and perpendicular vector projections of p(t) onto the vector î + j. (b) Find the distance from the boat to the shore at time t. (c) Find rate of change of the distance from the boat to the shore, then find the range of time when the boat is moving towards shore.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Suppose a lake is modelled by the region y – x > 0 in the plane. The shore is the straight line y – x = 0.
Suppose a boat travels on the lake with position vector p(t) = ti + (1+t²)j at time t > 0.
(a) Find the parallel and perpendicular vector projections of p(t) onto the vector i + j.
(b) Find the distance from the boat to the shore at time t.
(c) Find rate of change of the distance from the boat to the shore, then find the range of time when the boat
is moving towards shore.
Transcribed Image Text:Suppose a lake is modelled by the region y – x > 0 in the plane. The shore is the straight line y – x = 0. Suppose a boat travels on the lake with position vector p(t) = ti + (1+t²)j at time t > 0. (a) Find the parallel and perpendicular vector projections of p(t) onto the vector i + j. (b) Find the distance from the boat to the shore at time t. (c) Find rate of change of the distance from the boat to the shore, then find the range of time when the boat is moving towards shore.
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