lecture1_ex2.jl

md"""
## Exercise 2 — **Car travel in 2 dimensions**
"""

#md # 👉 [Download the notebook to get started with this exercise!](https://github.com/eth-vaw-glaciology/course-101-0250-00/blob/main/exercise-notebooks/notebooks/lecture1_ex2.ipynb)
#md #

#md # \warn{Write a monolithic Julia script to solve this exercise in a Jupyter notebook and hand it in on Moodle ([more](/homework)).}

md"""
The goal of this exercise is to familiarise with:
- code structure `# Physics, # Numerics, # Time loop, # Visualisation`
- array initialisation
- 2 spatial dimensions
- solving ODEs
"""

md"""
Based on the experience you acquired solving the [Exercise 1](#exercise_1_-_car_travel) we can now consider a car moving within a 2-dimensional space. The car still travels at speed $V=113$ km/h, but now in North-East or North-West direction. The West-East and South-North directions being the $x$ and $y$ axis, respectively. The car's displacement in the West-East directions is limited to $L=200$ km. The speed in the North direction remains constant.

Starting from the 1D code done in [Exercise 1](#exercise_1_-_car_travel), work towards adding the second spatial dimension. Now, the car's position $(x,y)$ as function of time $t$ has two components.
"""

#nb # > 💡 hint:
#nb # > - Split velocity magnitude $V$ into $x$ and $y$ component
#nb # > - Use `sind()` or `cosd()` functions if passing the angle in _deg_ instead of _rad_
#nb # > - Use two vectors or an array to store the car's coordinates
#nb # > - Define the y-axis extend in the plot `ylims=(0, ttot*Vy)`

#md # \note{- Split velocity magnitude $V$ into $x$ and $y$ component
#md # - Use `sind()` or `cosd()` functions if passing the angle in _deg_ instead of _rad_
#md # - Use two vectors or an array to store the car's coordinates
#md # - Define the y-axis extend in the plot `ylims=(0, ttot*Vy)`}

md"""
### Question 1

Visualise graphically the trajectory of the travelling car for a simulation with time step parameter defined as `dt = 0.1`.
"""