Results 1 to 2 of 2

Math Help - velocity, acceleration vectors

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    1

    velocity, acceleration vectors

    I have two questions.

    "As a figure skater spins, she raises and lowers her fingertip. This moving point has the parametrization
    r(t)=<x,y,z>=<2Cos(2t), 2Sin(2t), 3 + 2t - t^2>
    (The units are in feet and seconds.)
    If a ring slips off her finger at time t=0 and falls due to gravity, write a parametric equation for the motion of this falling projectile."

    I found the velocity vector to be v(t)=<-4sin(2t), 4cos(2t), 2-2t>. The position vector was given...and then I kinda got stuck.

    And for the second question:

    "What launch speed C is needed in order to kick a football over a goalpost that is 10 feet high and 100 feet away? Assume the launch angle is alpha=45 degrees. Use g=32 ft/sec^2. Solve for C in units of ft/sec.
    Hint. The projectile motion is described by
    x= Ct Cos(alpha)
    and
    y= Ct Sin(alpha) - 1/2g*t^2."

    I drew a triangle and used the pythagorean theorum to find the hypotenuse to be 100.5, then found the value of sin(45) to be .707...and plugged in 100.5*.707 (aka, 71.1) into the x equation for C...and I can't really follow what I did after that. I ended up getting 71.1 ft/sec, which was wrong.

    Thanks for your help! :-)
    -bree
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,692
    Thanks
    450
    Quote Originally Posted by bree56 View Post
    I have two questions.

    "As a figure skater spins, she raises and lowers her fingertip. This moving point has the parametrization
    r(t)=<x,y,z>=<2Cos(2t), 2Sin(2t), 3 + 2t - t^2>
    (The units are in feet and seconds.)
    If a ring slips off her finger at time t=0 and falls due to gravity, write a parametric equation for the motion of this falling projectile."

    I found the velocity vector to be v(t)=<-4sin(2t), 4cos(2t), 2-2t>. The position vector was given...and then I kinda got stuck.

    And for the second question:

    "What launch speed C is needed in order to kick a football over a goalpost that is 10 feet high and 100 feet away? Assume the launch angle is alpha=45 degrees. Use g=32 ft/sec^2. Solve for C in units of ft/sec.
    Hint. The projectile motion is described by
    x= Ct Cos(alpha)
    and
    y= Ct Sin(alpha) - 1/2g*t^2."

    I drew a triangle and used the pythagorean theorum to find the hypotenuse to be 100.5, then found the value of sin(45) to be .707...and plugged in 100.5*.707 (aka, 71.1) into the x equation for C...and I can't really follow what I did after that. I ended up getting 71.1 ft/sec, which was wrong.

    Thanks for your help! :-)
    -bree
    r(t)= \left<x,y,z\right>= \left<2\cos(2t), 2\sin(2t), 3 + 2t - t^2\right>

    v(t)= \left<-4\sin(2t), 4\cos(2t), 2-2t\right>

    as the ring leaves, it experiences a acceleration g only in the vertical direction , assumed to be z .

    r(0) = \left<2,0,3\right>

    v(0) = \left<0,4,2\right>

    for the ring, t \ge 0 ...

    v(t) = \left<0,4,2-gt\right>

    r(t) = \left< 2, 4t , 3 + 2t - \frac{1}{2}gt^2 \right>
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 5th 2011, 01:54 PM
  2. velocity and acceleration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 2nd 2011, 11:44 AM
  3. Velocity and Acceleration
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 28th 2009, 11:37 AM
  4. Velocity and acceleration
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 27th 2009, 01:54 PM
  5. Velocity and Acceleration
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 1st 2008, 07:30 PM

Search Tags


/mathhelpforum @mathhelpforum