# Random projectile motion problems.

1. Sep 8, 2009

### Jebus_Chris

1. Trajectory of a projectile is modeled by
$$r(t) = x(t)i+y(t)j$$
$$x(t) =at^2+bt$$
$$x(t) =ct+d$$
It asks for the displacement between t = 1 and t=3 s.
And I got
$$x(t)=8a+2b$$
$$y(t)=2c$$
If it is asking for the displacement would the answer be$$x+y$$ or $$\sqrt{x^2+y^2}$$?

2. The ball falls down from height h (above incline) on incline with angle 45. Calculate how far from striking point, ball will hit incline again if collision is perfectly elastic.

So the velocity it gains from falling would be $$\sqrt{2gh}$$. That would be the initial velocity of when it reflects at 0 degrees. Then you could create the projectile motion equations for it.
$$x=\sqrt{2gh}t$$
$$y=\frac{1}{2}gt^2$$
It will land when the x and y distances are equal. So after replacing the y with x, solving for t in terms of x, and substituting I got x=4h=y. So then the displacement would be $$\sqrt{8}h$$. That right?
Now I originally did this as the ball reflecting at 45(><) and i got $$x=hcos^2\theta (tan^2\theta - 1)$$ That gives you zero but you know that it would eventually hit the ground, why is that?

Last edited: Sep 8, 2009