Any Angle Projectile Motion Homework Market

 
  1. A) a student used the equations of motion to model the behaviour of a ball when kicked at different angles to the horizontal. She predicted the height of the ball when it reached the goal, presuming it was kicked from the same place, with the same initial speed, each time. The results are shown below:

    Angle Height
    10 -0.78
    20 1.0
    30 2.8
    40 4.7

    i) State the significance of the negative value of height at an angle of 10.

    B)
    i) During a football match the ball is kicked towards the goal, at an angle of 15 degrees to the horizontal, from a distance of 11m as shown.
    The ball has a diameter of 0.22m and an initial speed of 26ms-1. The goal is 2.4m tall.
    By means of calculations, determine whether or not the ball will pass into the goal. You may ignore the effects of air resistance.

    Last edited by lonerfish; 15-11-2015 at 22:01.
  2. Hello,

    For your first question, the idea is that essentially the ball has hit the ground before reaching the goal. The equations of motion do not account for the presence of the ground and therefore return a negative result for the eventual height.

    As for your second question, you should try and obtain the time that it takes for the ball to reach the goal by resolving horizontally. It is then possible to use the equation,



    to calculate the height of the ball's centre above the ground when the posts are reached. You should then add the radius of the ball in order to obtain the upper bound of the ball's position. This can then be compared to the height of the goal and then you can judge whether or not the ball goes in.
    (Original post by lonerfish)
    A) a student used the equations of motion to model the behaviour of a ball when kicked at different angles to the horizontal. She predicted the height of the ball when it reached the goal, presuming it was kicked from the same place, with the same initial speed, each time. The results are shown below:

    Angle Height
    10 -0.78
    20 1.0
    30 2.8
    40 4.7

    i) State the significance of the negative value of height at an angle of 10.

    B)
    i) During a football match the ball is kicked towards the goal, at an angle of 15 degrees to the horizontal, from a distance of 11m as shown.
    The ball has a diameter of 0.22m and an initial speed of 26ms-1. The goal is 2.4m tall.
    By means of calculations, determine whether or not the ball will pass into the goal. You may ignore the effects of air resistance.


I've found equations http://www.physicsclassroom.com/Class/1DKin/U1L6a.cfm for solving everything (and rearranged to solve everything) to do with projectile motion EXCEPT this, even though it should be possible.

  • Gravity = 10 m/s^2 (for simplicity)
  • Launch Angle = any angle in 0-360 degrees
  • Launch Position in x,y coordinates = any position, could be a different elevation than landing position
  • Landing position in x,y coordinates = any position other than Launch position, could be a different elevation than launch position

What is the general equation to solve for initial velocity for all angles 0-360 to hit a target at x2,y2 when launching from x1,y1?

Note: depending on the direction you are launching the projectile, some angles will not be possible, but keep in mind that if you were at a very high altitude and were launching a projectile at a target beneath you, launch angles other than 0-180 will be viable.

Just to be clear, this is the orientation of the 360 degree wheel I'm talking about, which has 90 degrees at the top and 270 at the bottom:

homework-and-exercisesnewtonian-mechanicskinematicsnewtonian-gravityprojectile

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