As it passes over Grand Bahama Island, the eye of a hurricane is moving in a dir

Question

As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 60.0 degrees north of west with a speed of 41.0 km/h.

a) What is the unit vector expression for the velocity of the hurricane? It maintains this velocity for 3.00 h, at which times the course of the hurricane suddenly shifts due north , and its speed slows to a constant 25.0 km/h. This new velocity is maintained for 1.50h.

b) What is the unit-vector expression for the new velocity of the hurricane?

c) What is the unit-vector expression for the displacement of the hurricane during the first 3.00 h?

d) What is the unit-vector expression for the displacement of the hurricane during the latter 1.50 h?

e) How far from Grand Bahama is the eye 4.50h after passes over the island?

Explanation / Answer

a) unit vector = cos@ i + sin@ j

@ is the angle of vector from +x -axis counterclockwise.

so here +ve x-axis means east

angle from east @ = 180 - 60 = 120 degrees

unit vector = cos120 i + sin120 j = - 0.5i + 0.866 j   

b) new velocity is along north.

so unit vector = 0i + 1j

C) during 3 hr velocity was 60 degrees north of west.

so displacement will be in the same direction as velocity ( v = r / t)

as calculated in (a)

displacement unit vector wil be same = - 0.5i + 0.866 j

D) finally it moves along north

so = 0i + 1j

E) r = r1 + r2

and r = vt

r1 = v1 t = 41 ( - 0.5i + 0.866 j ) x 3 = - 61.5i + 106.52j km

r2 = 25 ( 0i + 1j ) x 1.50 =37.5 j km

r = r1 + r2 = - 61.5 i + 144.02 j km

distance = sqrt ( 61.5^2 + 144.02^2) = 156.60 km

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