|
Question 1126973: Hi, I read this questions and came up with the equation, but I'm not sure if I did it right, can you help me?
======================
How far can a soccer player kick a soccer ball down field? Through the application of a linear function and a quadratic function and ignoring wind and air resistance one can describe the path of a soccer ball. These functions depend on two elements that are within the control of the player: velocity of the kick (vk) and angle of the kick (θ). A skilled high school soccer player can kick a soccer ball at speeds up to 50 to 60 mi/h, while a veteran professional soccer player can kick the soccer ball up to 80 mi/h.
*During the game the air and wind resistance play a role in the ball's path, however these factors make the equation more complex.
*The soccer ball in flight follows a parabolic curve.
** so basically it's like a right triangle with "Vk = Vkick" on the hypotenuse, "Vy" on the opposite side and "Vx" on the adjacent side. And a 0 in front of the acute angle between the hypotenuse and the adjacent side.
Vectors --> The vectors identified in the pattern describe the initial velocity of the soccer ball as the combination of a vertical and horizontal velocity.
Gravity --> The constant g represents the acceleration of any object due to the Earth's gravitational pull. The value of g near Earth's surface is about -32 ft/s^2.
Vx = Vk cos 0 and Vy = Vk sin 0
1. Use the information above to calculate the horizontal and vertical velocities of a ball kicked at a 35 degree angle with an inital velocity of 60mi/h. Convert the velocities to ft/s.
***so the equation would be 60 = 35 cos -32, which would be 0, so the x value is 0. and then the second equation would be -32 = 60 sin 35 = 34.4
2.The equations x(t) = vx t and y(t) = vy t + 0.5 gt^2 describe the x- and y- coordinate of a soccer ball function of time. Use the second to calculate the time the ball will take to complete its parabolic path.
Do I plug in (0,34.4)?
3. Use the first equation given in Question 2 to calculate how far the ball will travel horizontally from its original position.
??
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
\ =\ V_xt)
\ =\ V_yt\ -\ 16t^2)
For your given data
\ =\ (60\cos\,35^\circ)t)
\ =\ (60\sin\,35^\circ)t\ -\ 16t^2)
Remember, ) is positive when the ball is in the air, but gravity is pulling it down, hence the  acceleration due to gravity.
The ball will be at zero feet above the ground, i.e., \ =\ 0) at two times: one at  , the instant that the ball is kicked, and the other when it has completed its path.
Solve
\ =\ 0)
and select the non-zero root as the answer to question 2, and then evaluate ) for that value of  to get the answer to question 3.
John
My calculator said it, I believe it, that settles it
|
|
|
| |
