(11 %) Problem 9: A ship sets sail from Rotterdam, The Netherlands, intending to

Question

(11 %) Problem 9: A ship sets sail from Rotterdam, The Netherlands, intending to head due north at 9.5 m/s relative to the water. However, the local ocean current is 1.50 m/s in a direction 40.0° north of east and changes the ship's intended motion 50% Part (a) In what direction would the ship have to travel in order to have resultant velocity straight north relative to the earth, assuming the speed relative to the water remains 9.5 m/s? Specify the angle west of north, relative to the earth (i.c. A stationary obscrver on the shore). 50% Part (b) what would the ship's speed be relative to the Earth, in meters per second?

Explanation / Answer

Here ,

let the angle with the north is theta in west

velocity of ship relative to water , u1 = 9.5 * (-sin(theta) i + j * cosZ(theta))

local current velocity , u2 = 1.5 * (cos(40) i + j * sin(40)) m/s

a)

NOw, the net speed of ship relative to shore is

v = u1 + u2

v = 9.5 * (-sin(theta) i + j * cos(theta)) + 1.5 * (cos(40) i + j * sin(40))

for v to be in north direction

9.5 * sin(theta) - 1.5 * cos(40 degree) = 0

theta = 6.9 degree

the angle should be 6.9 degree west of north

b)

ship's speed = 9.5 * cos(6.9 degree) + 1.5 * sin(40 degree)

ship's speed = 10.4 m/s

the ship's speed relative to shore is 10.4 m/s

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