CaptainBlood Posted April 2, 2011 Share Posted April 2, 2011 A soccer player kicks a ball to his teammate, who is a distance d away. Even though the kick launches the ball with speed v0 and angle θ0 , the teammate knows it will not travel far enough to reach him before it lands. So as soon as the ball is kicked, the teammate begins running toward the ball. If he is to meet the ball just before it hits the ground, show that his average speed must be vp = (gd / 2v0 sin θ0) - v0 cos θ0 where g is the acceleration due to gravity. Neglect air resistance. I understand that t0 = tp and that the distance that the ball travels depends on the angle at which it is kicked. I solved for y to describe the trajectory of the ball in terms of angle theta and I know that xp = vp*t , then my plan was to solve the trajectory equation for x and use the fact that x0 + xp = d but I can't solve the trajectory equation for x since it quadratic. What do I do? Link to comment Share on other sites More sharing options...
Bignose Posted April 2, 2011 Share Posted April 2, 2011 ... but I can't solve the trajectory equation for x since it quadratic. you can't? http://en.wikipedia.org/wiki/Quadratic_equation Link to comment Share on other sites More sharing options...
CaptainBlood Posted April 2, 2011 Author Share Posted April 2, 2011 (edited) I know how to solve quadratic equations, it's just that when I try to solve this quadratic equation, the answer that I get is wrong and completely confusing. Here's the equation that I'm trying to solve y = y = (tan θ) x - g/(2(v0) (sin θ)^2) x^2 which describes the parabolic trajectory of a particle--in this case a soccer ball. Since theta is given to us and y = 0 when the ball hits the ground I was able to solve the quadratic now, but I don't know I tried to use the value I get for x0 , when I solved the quadratic, and plug that into the equation x0 + xp = d which is (cosθ sinθ (2v0)/g) - x0/v0cosθ = d and i get -1 = (gd / 2v0 sin θ0) - v0 cos θ0 which is close to what I'm trying to show but still not quite there. Edited April 2, 2011 by CaptainBlood Link to comment Share on other sites More sharing options...
swansont Posted April 2, 2011 Share Posted April 2, 2011 Why do you care about y as a function of x? Link to comment Share on other sites More sharing options...
CaptainBlood Posted April 2, 2011 Author Share Posted April 2, 2011 because y gives me the equation for the parabolic trajectory of the ball kicked at angle theta I made a mistake earlier in my algebra, but I took a look at my derivation again and it worked out beautifully. Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now