The eye of a hurricane passes over grand bahama island in a direction 60.0° north of west with a speed of 43.0 km/h. three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 23.0 km/h. how far from grand bahama is the hurricane 4.80 h after it passes over the island?

The hurricane will be 166.15km away from the island.

Explanation:

We can solve this problem with trigonometry and the formulas of constant velocity motion.

we need to find the displacement on the X and Y axis.

the speed on the X axis on the first trame of movemont is defined as:

we will take the reference to the left of the X axis as positive, so:

So the displacement on X is:

we will do the same for the Y axis:

the Y displacement is:

Then on the second trame of the movement we only have displacement on the Y axis.

now we need the total displacement on the X and Y axis:

The magnitud of the total displacement will be:

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y

490 n

f=125n a=2.5m/s2