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!

2D kinematics - Solved, but a question on the logic

  1. Jan 5, 2013 #1
    The problem: (Note: the correct answer is bolded throughout)

    A basketball is launched with an initial speed of 8 m/s at a 45 degree angle from the horizontal. The ball enters the basket in 0.96 seconds. What is the distance x and y?

    Just ignore the distance x, I know it's simply the product of the time and horizontal velocity.

    The distance y is obtained using the equation:

    y = (Vsin45)(t) + .5(-g)(t)^2
    y = 0.91m

    The above is the correct answer and how to obtain it--no quarrels there. My issue is why this method does not work:

    Here are my variables:

    t = Total time the ball is in the air
    Tp = The time for the ball to reach its peak height
    Tf = The time the ball is in free fall

    Tp = (Vsin45) / (g)
    Tp = (8sin45) / (9.8)
    Tp = 0.57723s

    Tf = t - Tp
    Tf = 0.96 - 0.57723
    Tf = 0.38277s

    y = .5(g)(t^2)
    y = .5(9.8)(0.38277^2)
    y = 0.72m

    The logic makes sense to me, since the ball takes .58 seconds to reach its peak height and obtain a velocity of 0 m/s. It should also then be in free fall for the remaining time (t-Tp) of 0.38s. I also thought that using the equation for displacement would be appropriate since only the acceleration due to gravity is present in the y direction. It is wrong however.

    If it helps, I'll also mention this problem was correctly solved using conservation of energy (0.91m), where the V in the final kinetic energy is obtained by using V horizontal, g, and the obtained Tf--so I know everything up until the displacement equation is correct.

    Could anyone enlighten me as to why I cannot use the displacement equation as I did?
     
  2. jcsd
  3. Jan 5, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Think about what that y you computed as 0.72 actually represents.
     
  4. Jan 5, 2013 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The value you get for y, 0.72m is the y value from the ball's peak height to the basket height. It should actually be -0.72m.

    What is the height gained by the ball in its first 0.57723 of flight?
     
  5. Jan 5, 2013 #4
    Ah, I completely neglected the fact it was traveling down from its peak and so the y represents how far the basket is from the top of its height.

    Thanks to you both! (I feel silly for ignoring that negative sign for gravity now)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: 2D kinematics - Solved, but a question on the logic
  1. 2D kinematic questions (Replies: 4)

  2. 2D Kinematics question (Replies: 3)

  3. 2D Kinematics Question (Replies: 6)

Loading...