1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Challenge Problem

  1. Oct 2, 2013 #1
    1. The problem statement, all variables and given/known data
    A person standing at the top of a hemispherical rock of radius R kicks a ball (initially at rest on the top of the rock) to give it a horizontal velocity v.
    What is the minimum initial speed to ensure the ball doesn't touch the rock?

    2. Relevant equations
    x^2 + y^2 = r^2
    y = -0.5gt^2 + R

    3. The attempt at a solution
    R - (gx^2)/(2v^2) > sqrt(R^2 - x^2).
    The left side is eqn for parabolic trajectory, the right is the boulder

    After a lot of math you get something like this:

    (g^2x^4) / (4v^4) + gRx^2 / v^2 + x^2 > 0

    Now I am super confused about this part:
    For some reason, the claim goes like, as x approaches 0, we get the tightest limit, therefore it needs the largest curvature at the start and it will pass the boulder (reasonable I guess..).
    THEN for some reason, 1 > gR / v^2

    I have no idea where this came from.

    See here; http://minerva.union.edu/labrakes/2_D_Motion_Problems_Solutions.pdf

    Another solution I read was;

    m * v^2/R > mg
    Fc > Fg.

    Why...? The acceleration into the boulder has to be GREATER than gravity?
    That doesn't make a lot of sense to me :(
  2. jcsd
  3. Oct 2, 2013 #2


    User Avatar

    Staff: Mentor

    At first glance, ISTMT you need the ball to travel at least R metres horizontally in the time that it takes to fall R metres vertically.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted