Homework after Class 4

Simulate Gravity

The last simulation we did in Class 4 was this:

N <- 60         # simulate 60 steps
y <- rep(NA, N) # create "empty" y vector
y[1] <- 120     # initial position
speed <- -20    # initial speed
for(i in 2:N) { # for each step
  y[i] <- y[i-1] + speed  # update position
  if(y[i] < -180 | y[i] > 180){ # if hit floor OR ceil
    speed <- -speed     # bounce
  }
}
plot(y)

• Modify this code to simulate gravity. Initial speed should be 0 and it must change by -1 on every step
• We want to make a plot to see how the speed changes. Make another version that saves the speed for each step. Now speed must be a vector. You have to insert the correct indices. It is similar to y.

You must send me one file in Rmd format with two pieces of code and two graphics.

Exercise (optional)

This is optional, but recommended to understand better. On Class 5 we will explore how things move when they are connected to an elastic rubber band.

{: .sidenote}

To be prepared, please read about

• Hooke’s law for springs
• Kinetic and Potential Energy

Good to know (optional)

When we use Scratch we can see a “movie” that is more fun than the graphics on R. Sometimes a movie can be a better way to explain an idea.

• Explore how can we animate graphics in R. Tell me something I don’t know.

Have you seen any of these movies?

• Gravity
• Apollo 13
• The Martian

What do they have in common?