Results 1 to 3 of 3

Math Help - Newtonian Mechanics 1

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    49

    Newtonian Mechanics 1

    A parachutist whose weight is 75 kg drops from a helicopter hovering 2000 m above the ground and falls towards the ground under the influence of gravity. Assume that the force due to the air resistance is proportional to the velocity of the parachutist, with the proportionality constant k1 = 30 kg/sec when the chute is close and k2 = 90 kg/sec when the chute is open. If the chute does not open until the velocity of the parachutist reaches 20 m/sec, after how many seconds will it be before the parachutist reach the ground? ( Take g = 9.81 m/sec2.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by bobey View Post
    A parachutist whose weight is 75 kg drops from a helicopter hovering 2000 m above the ground and falls towards the ground under the influence of gravity. Assume that the force due to the air resistance is proportional to the velocity of the parachutist, with the proportionality constant k1 = 30 kg/sec when the chute is close and k2 = 90 kg/sec when the chute is open. If the chute does not open until the velocity of the parachutist reaches 20 m/sec, after how many seconds will it be before the parachutist reach the ground? ( Take g = 9.81 m/sec2.)
    First find the time and height when the velocity reaches -20 m/s (here we take height x positive upwards) with the parachute closed. Then use the height time and speed as initial conditions for the final decent with the parachute open.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Mar 2009
    Posts
    256
    Thanks
    1
    Quote Originally Posted by bobey View Post
    A parachutist whose weight is 75 kg drops from a helicopter hovering 2000 m above the ground and falls towards the ground under the influence of gravity. Assume that the force due to the air resistance is proportional to the velocity of the parachutist, with the proportionality constant k1 = 30 kg/sec when the chute is close and k2 = 90 kg/sec when the chute is open. If the chute does not open until the velocity of the parachutist reaches 20 m/sec, after how many seconds will it be before the parachutist reach the ground? ( Take g = 9.81 m/sec2.)

    The equation of motion of the parachutist falling is :

    m\frac{dv}{dt} = mg-k_{1}v.................................................. ....................................1

    I hope you can derive that by applying the forces acting on the parachutist


    From (1) we have : \frac{mdv}{mg-k_{1}v} =dt

    And integrating from t=0 to t= t_{1} and from v=0 to v= 20m/sec we have :

    t_{1} =\frac{m}{k_{1}}ln\frac{mg}{mg-20k_{1}}

    And substituting the values given by the problem we find the time taken before the parachut opens .

    And since the equation for the motion is the same for the part where the parachut is open ,in a similar way you can calculate the time taken for this part ,and hence the overall time taken before the parachutist reach the ground
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. newtonian mechanics
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: June 4th 2010, 05:14 AM
  2. Newtonian Mechanics - the movement of a particles
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 6th 2010, 04:29 AM
  3. Newtonian Mechanics 2
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 1st 2010, 06:36 PM
  4. Newtonian mechanics vector notation
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: May 16th 2009, 08:01 AM
  5. Newtonian Method, just need algebra help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 21st 2007, 10:22 PM

Search Tags


/mathhelpforum @mathhelpforum