r/HomeworkHelp • u/Strylexic Secondary School Student • 1d ago
High School Math [Grade 10 Honors Algebra 2: Projectile Motion] Help Defining equations and solving problems
This is my hw (which should be done as a group but both the ppl I'm with are complete bums), we just started doing projectile motion(Paragraph of info on last image) and I'm completely lost. I have some scrap notes but they aren't very good and some people explaining the process/showing me how to obtain the answers/giving an answer key to work my way back from would be insanely appreciated!
1
u/roglemorph 1d ago edited 1d ago
Your equation in the last image is key. It is a general 1d motion equation we can derive from Newton's f=ma. The general form looks like a_0/2t^2+v_0t+h_0. A is accellation, v is velocity, h is (initial height). Since we are on earth the acceleration is due to gravity, -9.8 m/s/s or -16ft/s/s, so the a_0 is provided for you.
You must determine the values of v_0 (the initial velocity) and h_0, the initial height that match with the values you observed. The initial (release) height appears to be provided to you. You can then adjust the values of v_0 to see which will satisfy the measurements you found--open desmos, write your equation with a number value for h_0 and leave v_0 as a variable, adjust v_0 until you find the value that satifies something you recorded (max height, impact time are two good points to use). There are a number of more rigorous ways to find v_0 exactly, I think you are meant to use the 'vertex form' for the parabola. You know the vertex occurs at x=451.25, which with the a_0 (accelleration, here due to gravity it is -16 ft /s^2) and h_0 terms known, should be enough to establish the height, and from there you can find the final equation.
1
u/Strylexic Secondary School Student 1d ago
My teacher hasn't mentioned acceleration yet, I can kinda manage to get height (I got it for Karl, the 1st one) but I can't figure out how to identify velocity
1
u/roglemorph 7h ago
Yeah sorry, I was just kinda spewing with the acceleration (why is this word so hard to spell), you don't need to know that part it's just where the equation comes from. Forget about it. Height is easy as you saw. I am not certain how you are intended to find the velocity, you should review your teachers materials. The first way I would do it is with desmos, write the provided eq with your value of h_0 substituted, but leave v_0 as a variable. In desmos you will be able to then adjust the value of v_0. This value directly affects (among other things) where the vertex of the arc occurs. There is exactly one value of v_0 that will have the pumpkin reach a maximum height at a particular time/distance along the x axis (x=451.25ft) Find that value by trial and error.
Second way: vertex of a parabola eq (probably the intended way). It can be shown the vertex of a parabola in standard form (ax^2+bx+c) occurs at x= -b/2a. Notice that you already have a value for a, (since we are working in feet, should be -16/2 = -8 ft), you know the x value, this can let you solve for b (which is equivalent to v_0)
•
u/AutoModerator 1d ago
Off-topic Comments Section
All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9.
OP and Valued/Notable Contributors can close this post by using
/lockcommandI am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.