Results 1 to 5 of 5

Math Help - Projectile Motion Question

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    8

    Projectile Motion Question

    Alright, so I have the following projectile motion problem:

    A daredevil jumps a canyon 12 m wide, to do so, he drives a car up a 15 degree incline. What minimum speed must he achieve to clear the canyon, and if he jumps at this minimum speed, what will his speed be when he reaches the other side?

    I actually have the answer to the first question, I got it to be 15.46 using the two projectile launched at an angle formulas, subbing in 12.42/vi for t in the horizontal formula. What I'm looking for is how to solve the second part of the problem. Thanks for the help =)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Melbourne
    Posts
    428
    The speed will be exactly the same as the starting speed. An easy way to see this is by looking at the kinetic energy of the car: as the car rises, its kinetic energy is converted to gravitational potential energy, which is changed back into kinetic energy as the car goes down again. Since the car rises and falls the same distance, the same amount of energy is converted so the car ends up at the speed it started at.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2008
    Posts
    78
    You could try using to formula v^{2}_{x}=v^{2}_{0_{x}}+2a_{x}\Delta x

    where v^{2}_{x} is the final horizontal velocity, x^{2}_{0_{x}} is the initial horizontal velocity (plug in what you found for the first part here), a_x is the horizontal acceleration (im assuming this is zero?), and \Delta x is the horizontal displacement, or 12m in this case.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Aryth's Avatar
    Joined
    Feb 2007
    From
    USA
    Posts
    651
    Thanks
    1
    Awards
    1
    You're right, there is no horizontal acceleration since there are no horizontal forces mentioned.

    So, you have your formula:

    v_{0x}^2 = v_{fx}^2 + 2a_x \Delta x

    v_{0x}^2 = v_{fx}^2 + 2(0)\Delta x

    v_{0x}^2 = v_{fx}^2

    v_{0x} = v_{fx}

    But this is only in the x direction, the y-direction's change in velocity DOES affect the final velocity.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member TheMasterMind's Avatar
    Joined
    Dec 2008
    Posts
    155
    Quote Originally Posted by Crysolice View Post
    Alright, so I have the following projectile motion problem:

    A daredevil jumps a canyon 12 m wide, to do so, he drives a car up a 15 degree incline. What minimum speed must he achieve to clear the canyon, and if he jumps at this minimum speed, what will his speed be when he reaches the other side?

    I actually have the answer to the first question, I got it to be 15.46 using the two projectile launched at an angle formulas, subbing in 12.42/vi for t in the horizontal formula. What I'm looking for is how to solve the second part of the problem. Thanks for the help =)
    v sin15=y
    v cos15= x

    x y
    delta x=1/2at^2+vt delta y= 1/2at^t + vt
    delta x=vt 0=1/2(-9.8)t^2=vt
    12=v*cos15*t 0=-4.9t^2+v sin15 t
    12.37/v=t 0=-4.9(12.37/v)^2 + v sin15 (12.37/v)
    749.8/v^2 = v sin15 (12.37/v)
    749.8/v^2 = 3.20v/v
    749.8 = 3.20v^2
    239.3125=v^2
    15.46
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Projectile Motion Question #2
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: February 13th 2011, 07:49 PM
  2. Projectile Motion Question
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: February 13th 2011, 01:07 PM
  3. Projectile motion question
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 15th 2010, 03:00 AM
  4. Projectile motion question
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: November 10th 2009, 07:40 PM
  5. please check my answer - another projectile motion question
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: February 14th 2007, 02:04 PM

Search Tags


/mathhelpforum @mathhelpforum