Projectile Height

• A mass point launched from initial height $h_0$ (meters) with initial vertical velocity $v_0$ (m/s).

• Write a function height that takes $h_0$, $v_0$ and time $t$ (seconds) in all 64-bit floating point numbers and returns the height of the mass point at time $t$.

• In a mathematical expression,

$$ {\rm height}(h_0, v_0, t) = h_0 + v_0 t - \frac{1}{2}gt^2 $$

• where $g = 9.8$ [m/s${}^2$].

• Boilerplate source files {go,jl,ml,rs}/projectile_height.{go,jl,ml,rs} containing the test code is generated and shown below.

• Edit the source files either by opening them in a text editor (e.g., vscode), or editing the cells below and executing them.

1. AI tutor

1-1. Prepare

• Your personal AI tutor is provided for questions and feedback
• Execute the following cell before you use it

import heytutor

1-2. Examples

1-2-1. A general question

%%hey
How to write a function in Go?

1-2-2. A hint on this specific problem

%%hey
Give me a hint on this problem for Rust

1-2-3. NEW: A few builtin variables

• {file:FILENAME} is the content of FILE
• {bash[-1]} is the output of the last %%bash_ cell, {bash[-2]} that of the second last %%bash_ cell, etc.
• {problem} is the content of the file you specified by %%hey problem_file=foo.md
• {answer} is the content of the file you specified by %%hey answer_file=go/foo.go

1-2-4. Help when you struggle

%%hey answer_file=go/foo.go
I get this error when I compile it. What's wrong?"

My program:
{answer}

Error message:
{bash[-1]}

1-2-5. Ask feedback

• You are encouraged to ask a feedback once you think you are done with the problem, to know if there is a better answer. You can do so by something like:

%%hey problem_file=foo.md answer_file=go/foo.md
Give me a feedback to my answer.

Problem:
{problem}

My Answer:
{answer}

2. Go

2-1. Baseline code

import heytutor

%%writefile_ go/projectile_height.go
package main
import "fmt"
import "math"

/** begin my answer */
func height(h0, v0, t float64) float64 {
    return h0 + v0*t - 0.5*9.8*t*t
}
/** end my answer */

func main() {
    if !(math.Abs(height(10,  1, 1) - 6.1) < 1e-5) { panic("wrong") }
    if !(math.Abs(height(20,  0, 2) - 0.4) < 1e-5) { panic("wrong") }
    if !(math.Abs(height(30, -1, 3) - -17.1) < 1e-5) { panic("wrong") }
    fmt.Println("OK")
}

2-2. Compile

%%bash_
export PATH=${PATH}:~/.local/go/bin:~/go/bin
go build -o go/projectile_height go/projectile_height.go

• Note: when you run go or other Go commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/go/bin)
• You may consider adding that line in your ~/.bash_profile

2-3. Run

%%bash_
go/projectile_height

2-4. Ask Questions or Get Feedback

%%hey problem_file=projectile_height.md answer_file=go/projectile_height.go

Problem:
{problem}
My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.

3. Julia

3-1. Baseline code

import heytutor

%%writefile_ jl/projectile_height.jl
### begin my answer

height(h0, v0, t) = h0 + v0 * t - 0.5 * 9.8 * t * t
### end my answer

function main()
    @assert abs(height(10,  1, 1) - 6.1) < 1e-5
    @assert abs(height(20,  0, 2) - 0.4) < 1e-5
    @assert abs(height(30, -1, 3) - -17.1) < 1e-5
    println("OK")
end

main()

3-2. Compile

• Julia code is compiled "just in time" (compiled upon executed), so does not need a specific action for compilation before you run

3-3. Run

%%bash_
export PATH=${PATH}:~/.juliaup/bin
julia jl/projectile_height.jl

• Note: when you run julia or other Julia commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/.juliaup/bin)
• You may consider adding that line in your ~/.bash_profile

3-4. Interactive execution

• julia command also serves is an interactive command for Julia programs

• You can run a source code and continue interaction

$ julia -i jl/projectile_height.jl

• For trial and error, you may also consider creating a Julia notebook

3-5. Ask Questions or Get Feedback

%%hey problem_file=projectile_height.md answer_file=jl/projectile_height.jl

Problem:
{problem}

My Answer (between ### begin my answer and ### end my answer):
{answer}

Give me a feedback to my answer.

4. OCaml

4-1. Baseline code

import heytutor

%%writefile_ ml/projectile_height.ml
(** begin my answer *)

let height h0 v0 t = h0 +. v0 *. t -. 0.5 *. 9.8 *. t *. t;;
(** end my answer *)

let main () =
  assert (abs_float (height 10.0  1.0   1.0 -.   6.1) < 1e-5);
  assert (abs_float (height 20.0  0.0   2.0 -.   0.4) < 1e-5);
  assert (abs_float (height 30.0 (-1.0) 3.0 -. -17.1) < 1e-5);
  Printf.printf "OK\n"
;;

main()

4-2. Compile

%%bash_
eval $(opam env)
ocamlc ml/projectile_height.ml -o ml/projectile_height

• Note: when you run ocamlc or other OCaml commands (see below) in a terminal (SSH or Jupyter terminal), you need to execute the first line (eval $(opam env))
• You may consider adding that line in your ~/.bash_profile

4-3. Run

%%bash_
ml/projectile_height

4-4. Interactive execution

• ocaml command is an interactive command for OCaml programs

• In terminal (Jupyter or SSH), you can directly run a source code

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml ml/projectile_height.ml

• You can run a source code and continue interaction

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml -init ml/projectile_height.ml

• For trial and error, you may also consider creating an OCaml notebook

4-5. Ask Questions or Get Feedback

%%hey problem_file=projectile_height.md answer_file=ml/projectile_height.ml

Problem:
{problem}

My Answer (between (** begin my answer *) and (** end my answer *)):
{answer}

Give me a feedback to my answer.

5. Rust

5-1. Baseline code

import heytutor

%%writefile_ rs/projectile_height.rs
/** begin my answer */

fn height(h0: f64, v0: f64, t: f64) -> f64 {
    h0 + v0*t - 0.5*9.8*t*t
}
/** end my answer */

fn main() {
    assert!((height(10.0,  1.0, 1.0) -   6.1).abs() < 1e-5);
    assert!((height(20.0,  0.0, 2.0) -   0.4).abs() < 1e-5);
    assert!((height(30.0, -1.0, 3.0) - -17.1).abs() < 1e-5);
    println!("OK");
}

5-2. Compile

%%bash_
. ~/.cargo/env
rustc rs/projectile_height.rs -o rs/projectile_height

• Note: when you run rustc or other Rust commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (. ~/.cargo/env)
• You may consider adding that line in your ~/.bash_profile

5-3. Run

%%bash_
rs/projectile_height

5-4. Ask Questions or Get Feedback

%%hey problem_file=projectile_height.md answer_file=rs/projectile_height.rs

Problem:
{problem}

My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.