1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Free fall question

  1. Sep 18, 2006 #1
    Here's the question: A ball is dropped from rest from the top of a cliff that is 24 m high. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of teh second ball is exactly the same as that with which the first ball eventually hits the ground. In the absence of air resistance, the motions of the balls are just the reverse of each other. Determine how far below the top of the cliff the balls cross paths.

    For the first ball, I said that the vo = 0, and by using the formula v^2 = vo^2 + 2ax, I found that the v = 21.7 m/s. I then applied this to the second ball, making its vo = 21.7 m/s. Here is where I became stuck.

    I'm not sure how to find out where they cross paths - I figure I have to use simulataneous equations of some sort, but am not sure what variable I should solve for.
  2. jcsd
  3. Sep 18, 2006 #2


    User Avatar
    Homework Helper

    Try to visualize the problem - how far did both of the balls travel until their paths crossed? This will give you an equation which you can solve for t and retrieve your solution.
  4. Sep 18, 2006 #3
    I know that both of them will share the same t, but that still doesn't make any sense to me.
  5. Sep 18, 2006 #4


    User Avatar
    Homework Helper

    Of course they share the same time, but it's important that they 'swept' the length of 24m together. So, x1(t0) + x2(t0) = 24.
  6. Sep 19, 2006 #5
    Ok, so I'm still pretty confused. I'm trying to work this out, and I've made this into a system of equations. Maybe you can take a look:

    24-x = 1/2 (9.8)t^2 + 21.7t
    x= 1/2(-21.7t) + 0

    I know this is wrong, so I'm just confused where in my equations I'm wrong. Thanks again.
  7. Sep 19, 2006 #6


    User Avatar
    Homework Helper

    There is no x in your equation, only the time, t. Write down the equation of displacement for every ball, and then use the equation x1(t) + x2(t) = 24 (where x1(t) and x2(t) are the equations of motion for each ball, separately; one contains -g, and the other g). x mustn't confuse you; x is only the name of a function that depends on the time variable, t. We could have called it Z(t), or p(t), it really does not matter. x(t) is just a more conventional form.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Free fall question
  1. Free Fall Questions (Replies: 2)

  2. Free Fall Question (Replies: 4)