1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Physics Kinematics Problem.

  1. Sep 17, 2010 #1
    1. The problem statement, all variables and given/known data

    A ball is thrown straight upward and rises to a maximum height of y above its launch point. Show that the velocity of the ball has decreased to a factor α of its initial value, when the height is y2 above its launch point is given by y2=(1-α^2)y.
    Also SHOW that y2=(1-α^2)y.

    2. Relevant equations
    y=vt+1/2at^2, where a=-9.8m/s^2
    v1=v0+at (maybe)

    3. The attempt at a solution
    I've already attempted a solution that involves plugging in y=vt +1/2at^2 and did a bunch of algebra; I was writing so fast I probably did something illegal; one thing i was worried about was plugging in (v1-v0)/t for the acceleration, and canceled out the t^2. I also attempted a solution that involved looking at derivatives of both sides. That is, y2' = ((1-α^2)y)' with respect to t, after plugging in the aforementioned equation of kinematics.

    After all the algebra was said and done, I ended up with .5v(final)t+.5v(initial)t=y2, which definitely sounds incorrect to me.
    Is there a way to modify the kinematics equation y=vt+1/2at^2 to include y2?
  2. jcsd
  3. Sep 17, 2010 #2


    User Avatar
    Homework Helper

    Be careful with the notations. If you use y for the height in terms of t denote the maximum height by something else, say ym. Also, vt in the equation for y(t) should be v0t. So the correct form of the first equation is y=v0t+1/2*at^2.
    The equation for the velocity as function of time is correct in the form v=v0t + at.

    Plug in a=-g for the acceleration and work further with the new equations.

    You have to prove that when the velocity is v=αv0 the height is y=ym(1-α^2).

    That is almost all right! But you cancel out t if you plug in t=(v-v0)/a for t in the first equation. Then you will get the height y in terms of v instead of t.

    Can you proceed?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook