#### Assignment 2: Moving rockets

This assignment is due on Wednesday, 1/17 at 11:59 PM. Submit it using the handin server as assignment a2.

Let’s use what we’ve learned to animate a rocket launch.

We’ll solve this problem in two parts, horizontal and vertical, then combine them. The examples we animated in class and in the textbook prologue can guide us to solve both parts of the problem. This divide-and-conquer approach is possible because force applied along one axis to a moving body only affects motion along that axis and not any other axis. So the horizontal motion of a rocket is decoupled from its vertical motion, and we can write down two completely independent equations. Only the equation governing vertical motion involves gravity.

First make sure that you require the 2htdp/image and 2htdp/universe libraries.

Your program will animate a rocket fired with an initial speed init-speed and initial angle to the horizontal init-angle.

Exercise 1 Define init-speed and init-angle as program variables. Use an initial speed of 1 and an initial angle of pi/4 to start. Once your program is running, you should try using different values to see how your animation behaves. Note here that we are using an angle specified in radians.

Since only the initial speed will be specified, you will need to calculate the x and y components of the initial velocity. These may be calculated via

init-x-vel = init-speed * cos(init-angle)

init-y-vel = init-speed * sin(init-angle)

Exercise 2 Define the initial vertical velocity init-x-vel and the initial horizontal velocity init-y-vel using the initial speed init-speed and the initial angle init-angle. We define the initial speed and velocity components (horizontal and vertical) as numbers rather than functions because they do not change over time.

The rocket experiences a gravitational acceleration in the vertical direction. Therefore, the vertical position of the rocket is this function of the time t:

vertical position = init-y-vel * t - 1/2 * 0.002 * t * t

where init-y-vel is the initial velocity in the vertical direction, and 0.002 is the gravitational acceleration, which is a constant.

Exercise 3 Design a function y-pos which calculates the vertical position as a function of time t.

The rocket does not experience any acceleration in the horizontal direction. Therefore, it has constant horizontal velocity, and the horizontal position is a simpler function of the time t:

horizontal position = init-x-vel * t

Exercise 4 Design a function x-pos that calculates the horizontal position as a function of time t.

y = scene-height - h

Exercise 6 Finally, combine all of these functions together into a single function launch that draws an image at the correct horizontal and vertical positions, as a function of time t. Use this with the animate we discussed in class to produce an animation of a rocket launching with an initial angle to the horizontal and an initial speed.

You should see your rocket starting off at the lower left. It should then move up and right, and eventually, it should fall, but continue moving right, and eventually move off your scene.