Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
theEric
Group Title
(Classical Mechanics (with calc, but algebra could help)) Hi! I am stumped, but I feel like I should be able to get to the answer... A pitcher has a throwing speed that is a function of the angle the ball is thrown at. The problem is below, along with what I've thought of.
 8 months ago
 8 months ago
theEric Group Title
(Classical Mechanics (with calc, but algebra could help)) Hi! I am stumped, but I feel like I should be able to get to the answer... A pitcher has a throwing speed that is a function of the angle the ball is thrown at. The problem is below, along with what I've thought of.
 8 months ago
 8 months ago

This Question is Closed

theEric Group TitleBest ResponseYou've already chosen the best response.0
\(\sf\Large\color{orange}{The\ Problem}\) "A baseball pitcher can throw a ball more easily horizontally than vertically. Assume that the pitcher's throwing speed varies with elevation angle approximately as \(v_0cos\dfrac{1}{2}\theta_0\), where \(\theta_0\) is the initial elevation angle and \(v_0\) is the initial velocity when the ball is thrown horizontally. Find the angle \(\theta_0\) at which the ball must be thrown to achieve maximum (problem a:) height and (problem b) range." That's the part I need help with.. \(\sf\Large\color{orange}{My\ thoughts...}\) I've thought of using \(v_y = \left(v_0\ \cos\left(\dfrac{1}{2} \theta_0\right)\right)\sin\theta_0+gt\) and setting \(v_y=0\). I tried to do the same with \(v_y^2=v_0\ \cos\left(\dfrac{1}{2}\theta_0\right)+2gh\), but to no avail. I also thought of looking at \(y(t)\) and finding the maximum of its function, but that looks to difficult. I'm a slow learner, but I like to learn! Thanks for any help!
 8 months ago

PhysicsGuru Group TitleBest ResponseYou've already chosen the best response.1
(A) You can use \[V_{yfinal}^2 = V_{yinitial}^2 + 2(g)(Y_{final} Y_{initial}) \] where \[V_{yfinal} = 0m , Y_{initial} = 0 m/s, V_{yinitial} = (v_0cos(\frac{1}{2} \theta_0))sin\theta_0\] and solve for Yfinal
 8 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
Thank you very much! I can't believe I missed that  especially after writing that equation down! Thank you!
 8 months ago

PhysicsGuru Group TitleBest ResponseYou've already chosen the best response.1
(B) You can find the time it takes to reach max height then multiple by two to get the total time in the air. Once you have the total time you can use the equation for average velocity in the xdirection to find the range: \[V_x = \frac{Range}{Total Time}\]
 8 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
Thank you very much :)
 8 months ago

PhysicsGuru Group TitleBest ResponseYou've already chosen the best response.1
your welcome
 8 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
Wait.. I have to reask this. We could find \(Y_\text{final}\), but not \(\theta_0\)! I have found \(Y_\text{fintal}\).
 8 months ago

PhysicsGuru Group TitleBest ResponseYou've already chosen the best response.1
From the look of the problem setup there are no numbers... it looks like you are finding a formula for \[\theta_0\]
 8 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
Right.. I have to solve for what \(\theta_0\) would be to attain a maximum height. And, after that, I have to solve for a \(\theta_0\) that would give the maximum range. They will both be functions of \(v_0\). I should be able to calculate \(\theta_0\) in each case by knowing \(v_0\) and using substitution. I posted a new question, if you want to look there!
 8 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.