Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Mimi_x3

  • 2 years ago

Projectile Motion: Two particles are projected simultaneously from \(A\) with the same velocity \(V\) at the angles of elevation \(\alpha\), \(\beta\) on a horizontal plane respectively. If they both pass through \(B\), one after time \(t_1\) and the other after time \(t_2\). (a) show that \(\alpha+ \beta\=\frac{\pi}{2}\) (b) Prove that \(4V^2 = g^2 (t_{1}^{2} + t_{2}^{2}\) Will draw diagram below

  • This Question is Closed
  1. Mimi_x3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1344001551890:dw|

  2. Mimi_x3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well how do i start? anyone able to give me a hint?

  3. Vaidehi09
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    proving part b is simple. use the formula for time of flight of a projectile: T = 2vsinx/g......for both the projectiles. so u'll have t1 = 2vsinA/g.........[A = alpha]............(i) t2 = 2vsinB/g.........[B = beta]..............(ii) now, the RHS of ur question has t1^2 + t2^2..........so do exactly that. first square both (i) and (ii) and then add those. and then simplify and arrange the terms as required in the question.

  4. Mimi_x3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok i got it. how about a?

  5. Mimi_x3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    for b its the touchdown velocity right?

  6. Vaidehi09
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    still working on that one..i just remember that if the range is same for 2 projectiles then their angles of projection are complementary. i don't remember the proof though. so trying to derive that. and for b, its the initial velocity....given as V.

  7. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Range is same. \[\frac{u^2 \sin2\alpha}{g} = \frac{u^2\sin 2\beta }{g}\implies \sin 2\alpha = \sin2\beta\] \[\implies 2\alpha = 2\beta\;or\; \pi - 2\alpha = 2\beta \implies \frac{\pi}2 = \alpha +\beta \]

  8. Mimi_x3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you!

  9. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.