Question

As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 61.0° north of west with a speed of 42.4 km/h. (Let i represent east and j represent north.) (a) What is the unit-vector expression for the velocity of the hurricane? km/hi km/h j It maintains this velocity for 3.20 h, at which time the course of the hurricane suddenly shifts due north, and its speed slows to a constant 25.2 km/h. This new velocity is maintained for 1.50 h (b) What is the unit-vector expression for the new velocity of the hurricane? km/h i km/h (c) What is the unit-vector expression for the displacement of the hurricane during the first 3.20 h km i km j (d) What is the unit-vector expression for the displacement of the hurricane during the latter 1.50 h? km i km (e) How far from Grand Bahama is the eye 4.70 h after it passes over the island? km

Hi guys so I tried to work on these but I'm not sure how to do it ..

Answer 1

a) the velocity vector makes 61 deg with the W

x- comp = -42.4 Cos(61) kmph

y-comp = 42.4 sin(61) kmph

unit vector = -Cos(61) i + Sin(61) j = -0.48 i + 0.87 j

b) the velocity is due North later 1.5 hrs

unit vector = + j kmph

c) velocity and displacement are in same direction

unit displacement vector : -0.48 i + 0.87 j km

d) unit displacement vector : + j km

e) first 3.2 hrs displacement = 42.4(-0.48 i + 0.87 j ) *3.2

= -65.13 i + 118.04 j   km

last 1.5 hrs displacement = 25.2 * j *1.5 = 37.8 j km

Total displacement = -65.13 i + 118.04 j + 37.8 j

= -65.13 i + 155.84 j km

distance moved in 4.7 hrs = sqrt( 65.13² + 155.84²) = 168.9 km