Results 1 to 4 of 4

Math Help - Vector-valued functions and motions in space

  1. #1
    Senior Member
    Joined
    Oct 2009
    Posts
    295
    Thanks
    9

    Vector-valued functions and motions in space

    A golf ball is hit with an initial speed of 116ft/sec at an angle of elevation of 45 degrees from the tee to a green that is elevated 45ft above the tee as shown in the diagram. Assuming that the pin, 369ft downrange, does not get in the way, where will the ball land in relation to the pin?

    I thought I knew how to do this problem my answer differs from the book's. Here's mine:

    Find time (t)
    x= (v_{0}cos\alpha)t \Rightarrow 369=(116cos45\deg)t \Rightarrow t=\frac{369}{(58\sqrt{2})}\approx 4.5

    Then to find y I did:

    y= y_{0}+(v_{0}sin\alpha)t-\frac{1}{2}gt^2\Rightarrow y=-45+(116sin45\deg )4.5-\frac{1}{2}(32)(4.5)^2
    \Rightarrow -45+369.11 -324=0.11

    The problem is that for the answer in the book they don't use -45 at all and their final answer is that the ball is 45.11 feet in the air when it reaches the pin 369 feet away and therefore goes past the pin.

    I don't understand why the fact that the tee is 45 feet lower than the green doesn't factor into the answer. Can someone explain this to me?
    Last edited by mr fantastic; February 8th 2010 at 12:34 AM. Reason: Edited post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    " y_0" is the initial height of the ball. Since the green is 45 feet higher than the ball, y_0 is +45, not -45.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    y0 should be 0 otherwise if y0 = 45 y would be 90.11 ft when it passes over the pin
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Oct 2009
    Posts
    295
    Thanks
    9
    Thanks. I realized my error this morning while brushing my teeth. The golfer is standing on on the y-axis. Therefore, y_{0} is 0. It didn't make sense earlier but I guess taking a break from it for a while cleared things up.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Vector-valued functions and motion in space #2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 17th 2010, 10:33 AM
  2. [SOLVED] Vector-valued functions and motion in space
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 17th 2010, 08:56 AM
  3. Vector-Valued functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 17th 2010, 08:31 PM
  4. Vector-Valued Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 4th 2009, 05:40 PM
  5. L_2 space for matrix-valued functions
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: December 25th 2008, 11:51 PM

Search Tags


/mathhelpforum @mathhelpforum