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Math Help - [SOLVED] ideal projectile motion (vectors) calc3

  1. #1
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    [SOLVED] ideal projectile motion (vectors) calc3

    travel time:
    a projectile is fired at a speed of 840 m/sec at an angle of 60 degree. how long will it take to get 21km downrange?



    here is what i did an its no where close to right. the answer was 50seconds i got no ideal how to get that. here is what i attempted to do.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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     <br />
v_0 = 840m/s<br />

     <br />
\alpha=60~degrees<br />

    21km=21000m

    Now Lets take horizontal component of velocity which remains constant
    (as the gravity is vertical)
    So
     <br />
V_x= Vcos(60) = \frac{v}{2}<br />

    Thus in time t the distance travelled
    = \frac{v}{2} \times t

    Now look the distance travelled horizontally is known as Downrange

    Thus

    \frac{840}{2} \times t= 21000

    Can you go ahead
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  3. #3
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    Quote Originally Posted by ADARSH View Post
     <br />
v_0 = 840m/s<br />

     <br />
\alpha=60~degrees<br />

    21km=21000m

    Now Lets take horizontal component of velocity which remains constant
    (as the gravity is vertical)
    So
     <br />
V_x= Vcos(60) = \frac{v}{2}<br />

    Thus in time t the distance travelled
    = \frac{v}{2} \times t

    Now look the distance travelled horizontally is known as Downrange

    Thus

    \frac{840}{2} \times t= 21000

    Can you go ahead

    ok so 21000 * 2 = 42k / 840 = 50

    i have no idea what equation you used to get that though..

    the book gives a eqaution:

    (2v sin(alpha)) /g = t

    not sure what equation u used?
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Legendsn3verdie View Post
    ok so 21000 * 2 = 42k / 840 = 50

    i have no idea what equation you used to get that though..

    the book gives a eqaution:


    not sure what equation u used?
    -First of all You must know that velocity is in the form as

     <br />
V^2= (vsin(\theta))^2+(vcos(\theta))^2<br />

    -Now The term vsin(\theta) is the value of velocity in the y direction(vertical direction)
    (use trignometry)

    -similarly vcos(\theta) is the value of velocity in the x(horizontal) direction

    -Now the velocity in x direction remains constant and its value in y direction is affected by acceleration

    - Since we were given
    +the value of velocity
    + the value of alpha
    + the horizontal distance covered (distance travelled by V_x ONLY)

    -We can use the general formula that

     <br />
Velocity~\times ~time=~distance<br />

    ie;

     <br />
V_x ~\times t = 21000m<br />

    Watch the diagram and this link
    Attached Thumbnails Attached Thumbnails [SOLVED] ideal projectile motion (vectors) calc3-components.bmp  
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