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Projectiles colliding on a horizontal plane

  1. Apr 12, 2013 #1
    1. The problem statement, all variables and given/known data
    A bullet is fired from a gun fixed at a point O with speed v m/s at an angle Θ to the horizontal, At the instant of firing , a moving target is 10m vertically above O and travelling with constant speed 42√ 2 m/s at a constant angle 45 degrees to the horizontal.The bullet and target move in the same plane.

    (i) if v = 70 m/s, show that if the bullet is to hit the target then tanΘ = 4/3

    (ii) Find at what time after firing does the bullet strike the target and calculate the horizontal distance of the bullet from O


    2. Relevant equations

    s=ut + (1/2)gt^2


    3. The attempt at a solution

    If they are to collide then there horizontal velocities must be equal.

    70cosΘ = 42√2(cos45) ............. cosΘ = 42/70 =3/5

    using Pythagoras' sinΘ = 4/5 and tanΘ = 4/3


    (ii) There height must be the same when they collide h1 = h2

    42√ 2(sin45)t - (1/2)gt^2 + 10 = 70(4/5)t - (1/2)gt^2

    (1/2)gt^2 cancel

    42t + 10 = 56t ...................... t = 10/14 seconds

    horizontal distance of the bullet from O 70(3/5)(10/14) = 30m

    My book says the answers for (ii) are 10/7 seconds and 60m.

    Can anybody spot if I went wrong at any point? Any help would be appreciated.
     
  2. jcsd
  3. Apr 12, 2013 #2

    TSny

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    Homework Helper
    Gold Member

    The target is not in free fall.
     
  4. Apr 12, 2013 #3
    Thanks I removed that -(1/2)gt^2 and got the right answer.
     
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