What is the Solution for Finding Velocity and Distance on a Water Slide?

[Clever_name]

the restriction on the possible angle would i assume range from 0-90, or 0 - pi/2?

I don't get what you're saying when you say divide by 2n.

I divide theta ≈ 0.74559 + 6.28319n by 2n? I don't see how that would help me see where the angle lies.

 

[Simon Bridge]

Not 2n, 2π - spot the difference.
Oh OK, I'll write more clearly:
Divide by $2\pi$.

To see why: what is $2\pi$ in decimal to oh... 5dp?

Why would there be more than one correct value for the angle?
Is the value periodic? Is so, what is the period?

Whatever - do not guess about the range of the allowable angle - use the problem statement to tell you.

 

[Clever_name]

2pi to 5 decimal points is 6.283185.

and the period is 6.283185, so the period is 2pi!

I'm looking at the problem statement and cannot see why the max allowable range wouldn't be 0-90, given that we are looking for the max change in distance x.

 

[Simon Bridge]

Sure - I directed you to check because you said you "assumed".
Don't "assume" unless donkeys are involved ;)

The ramp could, technically, have been built to any angle.
If the ramp angle were between 90 and 180, for eg., you'd get a long distance but in the opposite direction... so the displacement would be negative. (And it would have hit the hill before that distance was reached.)

What happens when the ramp angle is between 180 and 360? When would the next maximum be after 360 degrees - what does the ramp look like compared with the initial angles less than 90?

In this way the physics will tell you which of your available numbers make sense.
You could arrive at the same conclusion by maths, when you remember how many radians go in a full circle.

Note: you should start using radians by default, particularly for geometry and physical sciences.
It makes things a lot easier in the long run.

 

[SammyS]

Hi Simon! Try this link http://i49.tinypic.com/2vdh3yf.jpg to view a picture of the situation.

Did you know that you can display this image directly in your post?