A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 3 years ago
A particle during projectile motion reaches height h in time t1. Again it reaches this height 'h' in time t2 measured from start. Show that the height of point 'h' is 1/2 gt1t2.
 3 years ago
A particle during projectile motion reaches height h in time t1. Again it reaches this height 'h' in time t2 measured from start. Show that the height of point 'h' is 1/2 gt1t2.

This Question is Closed

y2o2
 3 years ago
Best ResponseYou've already chosen the best response.0what does it mean "from start" ?!

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1What's the equation of motion of the projectile? Let y be its height above the point from which it's thrown. Then \[ y(t) = v_0t  \frac{g}{2}t^2 \] Now you're told that for two values of time, \( t = t_1, t_2 \) \[ y(t_1) = y(t_2) = h \] Use these equations to solve for h.

arcticf0x
 3 years ago
Best ResponseYou've already chosen the best response.0Already did that, the problem is, how to merge t1, t2. And the equation of projectile is \[x \tan \alpha  gx ^{2}/2u ^{2}\cos ^{2}\alpha\]

arcticf0x
 3 years ago
Best ResponseYou've already chosen the best response.0thats the y component

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1The equation I've written down is just the vertical component, the y. And that's all you need. The x component isn't necessary.

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1Substitute t = t1 and t2 into that equation and you have two simultaneous equations in the variables v_0 and h. Now solve them for h.

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1I.e., \[ \frac{g}{2}t_1^2 + v_0 t_1 = h \] \[ \frac{g}{2}t_2^2 + v_0 t_2 = h \] Solve for h.

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1*dropped the minus sign on the g terms.

arcticf0x
 3 years ago
Best ResponseYou've already chosen the best response.0yeah i am almost there now. I eliminated v0 and the one equation is left in the terms i need. Its not rearraning easily but i will leave it to that because i have got the idea. Thanks again JamesJ!

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1Multiply the first equation by t_2; the second by t_1. Then subtract the second equation from the first and the v_0 terms will cancel.

arcticf0x
 3 years ago
Best ResponseYou've already chosen the best response.0You are a genius and a lifesaver, just cannot thank you enough! It worked :)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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.