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How to find initial velocity given distance and angle

  1. Jan 14, 2014 #1
    1. The problem statement, all variables and given/known data
    A projectile is fired with initial velocity Vo at an angle of 20° with the horizontal. Determine the required value of Vo if the projectile is to hit point b.
    point b is 3 km away.


    2. Relevant equations
    y=(Vy)o t + 1/2 a t^2


    3. The attempt at a solution
    i tried isolating time(t) from the above formula which gave me square root of 2y/a but i cant take the square root of a negative number that bring the acceleration
     
  2. jcsd
  3. Jan 14, 2014 #2
    Some hints: Draw the diagram and then use the formula. What do you know about the x-distance and y-distance?
     
  4. Jan 14, 2014 #3
    I have to multiply it by cos20 and sin 20
     
  5. Jan 14, 2014 #4
    Hi Tsukuba. Welcome to Physics Forums.

    What is the value of y when the projectile reaches the ground again? What is the acceleration "a" in your equation for y? Can you use your equation for y to figure out how much time the projectile is in the air?

    Chet
     
  6. Jan 14, 2014 #5
    hello and thank you.

    a=-9.81 m/s^2
    I can use the equation because i would have 2 unknowns, that being the initial velocity and time. Like i said I tried isolating time and the formula i get is square root of 2x/a and i cant take the square root of a negative number.
     
  7. Jan 14, 2014 #6
    As I see it, your equation for the y direction is going to be:
    [tex]0=v_0\sin(20)t-\frac{9.8}{2}t^2[/tex]
    Is this in agreement with your assessment? If so, you can solve this equation for t by factoring the right hand side, and discarding the root at t = 0. In terms of v0, what do you get for t?

    Chet
     
  8. Jan 14, 2014 #7
    instead of the 0 wouldn't i have the distance of 3km?
     
  9. Jan 14, 2014 #8
    here is the question and the diagram
    mec.png
     
  10. Jan 14, 2014 #9
    We are talking about the y direction here, not the x direction. When the projectile hits the ground, y = 0.
     
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