Question

As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 30◦ north of west with a speed of 51 km/h. Three hours later, it shifts due north, and its speed slows to 34 km/h. How far from Grand Bahama is the eye 4.50 h after it passes over the island? Answer in units of km.

Answer 1

Answer:183.52 km

Step-by-step explanation:

Given

First hurricane is moving in a direction
`30^(\circ)`

speed of hurricane =51 km/h

After 3 hr it changes its direction changes to North and speed decreasing to 34 km/h

Position vector of Hurricane after 3 h

`r_1=51* 3(-cos30\hat{i}+sin30\hat{j})`

After 1.5 hr position vector of hurricane w.r.t previous one

`r_(21)=34* 1.5(\hat{j})`

thus
`r_2=r_(21)+r_1`

`r_2=-132\hat{i}+127.5\hat{j}`

So total distance
`=|r_2|=√(132^2+127.5^2)`

`=√(33,680.25)=183.52 km`