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Trajectory question(find spped of impact)

  1. Sep 12, 2010 #1
    A golfer drives a ball with initial angle
    θ = 45 from a tee at the origin. The ball
    hits a window at height h = 10m a distance
    D = 80m away.

    a. Find the initial launch speed v0 of the ball.

    b. Suppose a second golfer tees off from the
    same spot at an unknown angle and speed,
    and miraculously her shot also hits the window
    at the same height 1.8 s after launch. With
    what speed did it hit the window?

    c. Was her ball ascending or descending or in level flight when it hit?




    y(x) = tan*x -.5*g*(x^2/v0^2*cos^2)



    part a was easy enough, i solved the above trajectory equation for v0 to get v0=30m/s, but after that i cant figure out how to solve part b and c. it seems everything i could solve for to get the velocity of impact requires knowing the initial angle and initial speed
     
  2. jcsd
  3. Sep 13, 2010 #2
    bump


    i am revisiting this problem currently, still having trouble with parts b and c
     
  4. Sep 13, 2010 #3
    all right, if this method does not have any critical errors in it, i believe i solved it(fingers crossed)


    so this is how i did it:

    since t =1.8seconds, i can find out the product of cosθ and v0

    x(t) = v0*cosθ*t

    80/1.8 = v0*cosθ

    44.45= v0*cosθ

    i can do similar for finding the product of v0 and sinθ from the formula

    y(t) = v0*sinθ*t - 1/2*g*t^2

    10 = v0*sinθ(1.8) - (1/2*9.8*1.8^2)

    10 + 15.88 = v0*sinθ(1.8)

    14.38 = v0*sinθ

    then i proceeded to use these figures in the velocity functions..

    vx(t) = v0*cosθ and vy(t) = v0*sinθ - gt

    first the horizontal velocity is just the same:


    44.45= vx(t)

    next, solving for vertical velocity

    vy(t) = v0*sinθ - gt

    = 14.38 - (9.8*1.8)

    vy(t)= -3.26 which is the answer for c, because it is negative acceleration, meaning heading back to earth i think

    next the speed of impact is given by formula:
    s = |v| = (vx^2+ vy^2)^1/2

    so [(-3.26)^2 + (44.45)^2 ] = 44.57 m/s, which is the answer to b

    is it right???? i hope so, but i am unsure of some of my math here
     
    Last edited: Sep 13, 2010
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