# Projectile Motion

For my mechanics, I am trying to model the flight of an objected released from an angled slide, which slides (not rolls) down a distance L (constant), launches at a hight h (constant) above ground and travels a distance X, untill it hits the ground. The slide's angle A is adjusted.

My problem is I cannot seem to come up woith a simple formula, the only way I find to solve this using SUVAT equationsd as i have been told to ,ends up in a hefty quadratic equation, and several people have noted that there are simpler ways to model this? Any links to sites containing similar problems, or Ideas on how to approach this, and what equations to use would be greatly appriciated!

http://www.skylinecomputers.co.uk/misc/Slide.JPG [Broken]

A quick diagram I knocked up...

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Integral
Staff Emeritus
Gold Member
At the point of exit from the tube the problem becomes a falling body problem, this can be seperated into x and y components of motion. The first step is to define your coordinate system,let the origin be the ground level below the lower end of the tube, let y be vertical and increasing up, let x be horizontal and increasing away from the end of the tube. The end of the tube is at y=h.

For the y or vertial motion you have:
$$\frac {d^2y} {dt^2} = -g$$
With initial condions
$$\frac {dy} {dt} \mid_0 = v_y$$
$$y(0) = h$$

for the x (horizontal motion) you have:
$$\frac {d^2x} {dt^2} = 0$$
With initial conditions:
$$\frac {dy} {dt} \mid_0 = v_x$$

The equation for the y motion is simply a statement that the object falls with constant acceleration. The equation for x motion is a statement of no acceleration or constant velocity.

The solution for the y motion is:
$$y(t) = -\frac 1 2 g t^2 + v_yt + h$$
The solution for the x motion is :
$$x(t) = v_x t$$

To get the initial velocity use conservation of energy,

$$mgd = \frac 1 2 m v^2$$
so
$$v = \sqrt {2gd}$$
d is the total drop of the tube.
Using trig we get
$$v_y = v \sin( \theta)$$
$$v_x = v \cos( \theta)$$
This is much more then I generally provide for this type of problem, but it is not clear what level you are working at (high school or college) I hope you can complete the problem by putting all the pieces together.

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HallsofIvy