Marko rides 10 km north of his home

on his mountain bike. He reaches an
abandoned railroad, turns through an angle
of 120° onto the railroad, and then rides
another 20 km.

and then gets hit by a train.

To find Marko's final location, we can break down his movement into the x-axis (east-west) and y-axis (north-south) components.

First, we need to determine the change in the x and y coordinates for his initial movement of 10 km north. Since he only moves in the y-axis, the change in the y-coordinate is 10 km, and the change in the x-coordinate is 0 km.

Next, we need to determine the change in the x and y coordinates for his movement along the abandoned railroad. Since he turns through an angle of 120° onto the railroad, we can imagine a triangle with the hypotenuse being the distance Marko rides along the railroad (20 km), and the vertical side being the change in the y-coordinate.

Using trigonometry, we can find that sin(120°) = change in y / 20 km. Solving for the change in y, we have change in y = sin(120°) * 20 km ≈ 17.32 km.

Now we can calculate the change in the x-coordinate using the same triangle. Since Marko moves in a straight line along the railroad, the change in the x-coordinate is equal to the distance Marko rides along the railroad, which is 20 km.

To find Marko's final location, we add up the changes in the x and y coordinates:

Final x-coordinate = initial x-coordinate + change in x-coordinate
= 0 km + 20 km
= 20 km east

Final y-coordinate = initial y-coordinate + change in y-coordinate
= 10 km + 17.32 km
= 27.32 km north

Therefore, Marko's final location is 20 km east and 27.32 km north of his home.