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!

Gravity (Kinematics)

  1. Jan 27, 2008 #1
    1. The problem statement, all variables and given/known data
    The acceleration of gravity can be measured by project a body upward and measuring the time that it takes to pass two given points in both directions. Show that if the time the body takes to pass a horizontal line A in both directions is Ta and the time to go by a second line B in both directions is Tb then assuming that the acceleration is constant, its magnitude is g = 8h/(Ta^2-Tb^2)

    2. Relevant equations
    y = y0 + 1/2 g t^2 + vot


    3. The attempt at a solution

    There is a diagram where A is the lower position and B is the higher position, they are separated by a distance h.

    I found Ta = -2/g vy and Tb = -vy +- sqrt(vy^2 - 2gh)
    but I really don't know where to go after this...
    If I want acceleration a = dv/dt and v = dx/dt but I'm not quite sure what to do next... If I say delta T = Ta - Tb but that's all i can get.
     
  2. jcsd
  3. Jan 28, 2008 #2

    mezarashi

    User Avatar
    Homework Helper

    You'll need 2 equations to solve this problem:

    1. Express the initial velocities Va and Vb as a function f(g,ta) and f(g,tb) respectively. This can be done using the s = vt + 0.5at^2 kinematics equation.

    2. Use the kinematics equation: Vb^2 = Va^2 + 2gh

    From equation 2, you can substitute out Vb and Va into a function purely of g and t. From there, it's just algebra. Good luck.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?