Question

As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 62.0° north of west with a speed of 39.4 km/h. (Let î represent east and ĵ represent north.) (a) What is the unit-vector expression for the velocity of the hurricane? It maintains this velocity for 3.10 h, at which time the course of the hurricane suddenly shifts due north, and its speed slows to a constant 26.8 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? (c) What is the unit-vector expression for the displacement of the hurricane during the first 3.10 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 4.60 h after it passes over the island?

Answer 1

Vector diagram for the given situation is shown below :

(a) Initial velocity of hurricane in unit vector notation can be written as

or, (in km/hr)

(b) The new velocity of hurricane in unit vector notation can be written as

(in km/hr)

(c) The direction of displacement will be same as the velocity.

First we have to calculate total displacement in first 3.10 hr. Which can be calculated as :

  

The vector diagram will look like ,

N: North i) 122.14 km 62.0 E East (i) W : West S: South

So, the unit vector notation for the displacement in first 3.10 hr can be written as

  

or, (in km)

(d) In the next 1.50 hr displacement of the hurricane will be

And again the displacement will be in north direction as the velocity.

So, in unit vector notation this displacement can be written as

   (in km)

(e) After 4.60 hr the net displacement of the hurricane will be

or,

So,

Hence, the eye is now 158.76 km far away from Grand Bahama.

For any doubt please comment.