Answer: 315 km
Step-by-step explanation:
If the angle θ is measured from the x-axis, and we have a magnitude A, we can find the rectangular coordinates as:
Ax = A*cos(θ)
Ay = A*sin(θ)
Then:
The first helicopter has a speed of 160km/h, and it's angle is 290°.
Then the components will be:
Vx = 160km/h*cos(290°) = 54.7 km/h
Vy = 160km/h*sin(290°) = -150.4 km/h
Then the point location as a function of time, can be written as:
(where i assumed that the initial position of both helicopters was (0, 0))
P1(t) = (54.7 km/h*t, -150.4 km/h*t)
where t is time in hours.
We can do the same for the other helicopter:
The speed is 100km/h, and the angle is 250°
Then:
Vx = 100km/h*cos(250°) = -34.2 km/h
Vy = 100km/h*sin(250°) = -94 km/h
Then the point location as a function of time, will be:
P2(t) = (-34.2km/h*t, -94 km/h*t)
After 3 hours, the position of each helicopter will be:
P1(3h) = (54.7 km/h*3h, -150.4 km/h*3h) = (163.1 km, -451.2 km)
P2(3h) = (-34.2km/h*3h, -94 km/h*3h) = (-102.6km, -282km)
Now we can calculate the distance between these two points.
Remember that the distance between the points (a, b) and (c, d) is:
D = √( ( a - c)^2 + (b - d)^2)
In this case the distance will be:
D = √( (163.1 km - (-102.6km))^2 + (-451.2 km - (-282km))^2)
D = √( (163.1 km + 102.6km)^2 + (-451.2 km + 282km)^2)
D = 315km
