Assignment 02

And so you can see that if we know width and length, we can find angle α from the first equation. Knowing α, and being able to measure angle γ, we can then calculate β from the second equation. Once we know all these quantities, we can locate the spot on the floor where the trajectory of the green goo (that's the red line) hits. Of course, we must know the height of the green goo spatter off the floor. We'll call this point on the floor the "origination point". For simplicity, let's say the coordinates of the origination point are v_x and v_y. We are seeking the origination point.

Let's start by rewriting the above equations as

(1) α = arcsin (width / length)

β = arctan (tan(α) / sin(γ))

Then, from trigonometry, we also find

(2) v_y = (height) * tan(α) note: * means multiplication

v_x = v_y * tan(β)

Thus you can see that with inputs of width and length of the spatter, the height of the spatter on the wall, and the angle γ, you can compute the origination point. But there is one other thing to know about alien blood. It is known that green goo will spread as it dries. So, to get an accurate measure of the dimensions of the spatter, you must subtract from the measurements of the width and length of the spatter that constant green goo expansion factor equal to 1 inch. (This should be part of your formulation.)

Specifications: Your program is to greet the user with a welcoming message such as "Welcome. You are running the GGPA program ...." or something similar. Next, it should prompt the user for inputs for

1. the height from the floor of the green goo spatter in whole inches (use an int-type for this variable)

2. the width of the spatter in inches (an int-type)

3. the length of the spatter in inches (an int-type)

4. the angle γ (refer to it as "gamma") in radians (use a float variable for this)¹

The program should then compute the values of v_x and v_y. Your output should be "user friendly" in the sense that you should, in some fashion, echo the inputs and present the resulting calculated values in a way that makes it easy to understand. Just outputting final numbers is not good enough:

5 and 8

See, there is no explanation of what those numbers are. Here's an example of good output:

You have input:

ht = 67

width = 5

length = 12

gamma = .9

The origination coordinates are x = 13.03 and y = 26.15

Your program (as all programs) should end with a signoff message.

Notes: You are going to need to compute the arcsin and arctan of values. This capability is included in the cmath library. In order for you to use it in your program, put #include <cmath> just after (or before) the other include you have in your program. Then, as an example, this code would store the value of the arcsin(.5) and arctan(.5).

float angle1, angle2;

angle1 = asin(0.5);

angle2 = atan(0.5);

These are function calls and we will learn more about functions in general in about 4 weeks.

When you submit: the submit script will compile and run your program during the submission process. Thus, you will be the "user" of the program and will have to enter information at your own prompts. Now, in order to NOT drive the grader nuts with different answers, you will ALL enter the same values. Thus,

• enter width 5

• enter length 10

• enter gamma 0.6 (radians)

• enter 72 (inches) for height

As usual, if you have any questions or concerns about this assignment, don't hesitate to ask your instructor or go for help at the LEAD sessions. Note: no little green aliens were harmed during the preparation of this web page. We might have offended some, but that's life.

¹I realize that it's a stretch that crime scene investigators know what radians are. Even many engineers don't know! So it goes....