Answer:
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:
[tex]Vx=V*cos(ang)[/tex]
we will take the reference to the left of the X axis as positive, so:
[tex]Vx=43*cos(60)\\Vx=21.5 km/h[/tex]
So the displacement on X is:
[tex]dx=Vx*t\\dx=21.5km/h*3h\\dx=64.5km[/tex]
we will do the same for the Y axis:
[tex]Vy=V*sin(ang)\\Vy=43sin(60)\\Vy=37.24km/h[/tex]
the Y displacement is:
[tex]dy=Vy*t\\dy=37.24km/h*3h\\dy=111.72km[/tex]
Then on the second trame of the movement we only have displacement on the Y axis.
[tex]dy2=Vy2*t\\dy2=23km/h*1.8h\\dy2=41.4km[/tex]
now we need the total displacement on the X and Y axis:
[tex]Y=dy+dy2\\Y=153.12km\\X=64.5km[/tex]
The magnitud of the total displacement will be:
[tex]D=\sqrt{(X)^2+(Y)^2}\\D=\sqrt{(64.5)^2+(153.12^2}\\ \\D=166.15km[/tex]
