Results 1 to 2 of 2

Math Help - Projectiles

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    2

    Question Projectiles

    If a bullet is fired from a gun at a point o with a speed of 150m/s at an angle Tan-1(3/4) to the horizontal.At the instant of firing,a moving target is 25.1 metres vertically above o and is moving at an angle of 45 degrees to the horizontal at a constant speed of 90root2 m/s.show that the bullet strikes the target after 1 second.where does the strike occur???assume there on the same plane.


    i got 85.1 ,but i didn't use all the info given so im not confident with the answer.Can anybody tell me what they got and how?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2008
    Posts
    148
    The horizontal initial velocity is

    v_x(0) = v(0)\cos(\theta) = 150(.6) = \text{ 90 m/s }

    and the vertical initial velocity is

    v_y(0) = v(0)\sin(\theta) = 150(.8) = \text{ 120 m/s }.

    The horizontal velocity remains the same throughout the bullets flight since there is no acceleration in the x-direction after the bullet is fire. But the velocity in the y-direction is changing because of the acceleration due to gravity. Initially this is downward (in the opposite direction of the vertical velocity) and the velocity as a function of time is governed by the equation: v_y(t) = v_y(0) a t where a = -9.81m/s^2.

    Also the x-position of the bullet is x(t) = v_x(t)t while the y-position is y(t) = v_y(0)t + 1/2at^2.

    So after 1 second the bullet has traveled x(1) = v_x(1)1 = 90 m/s (1 s) = 90m in the x-direction and y(1) = 90m/s(1 s) - 9.81/2(1)^2 = 115.095m in the y-direction. So you might say that the bullet is at the position (90,115.1)

    Now the target is moving 90 m/s in both the x and y directions. The speed is constant. so after 1 second the target has moved 90m vertical and 90m horizontal putting its position after 1 second at exactly (90,115.1), which is where the target is.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Projectiles
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: November 21st 2010, 08:13 AM
  2. Projectiles
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: January 8th 2010, 03:46 AM
  3. DEs and projectiles
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 20th 2009, 08:14 PM
  4. projectiles?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 16th 2009, 10:15 AM
  5. Projectiles again
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 4th 2009, 09:23 AM

Search Tags


/mathhelpforum @mathhelpforum