Need help with AP Physics Q Preferrably before 6AM

[dwangus]

Homework Statement

I'm so lost in class right now... can anyone go through step-by-step how to solve this problem?

A small mass moves along a friction free level surface (of height 10 meters) at a speed of 5m/s and comes to a circular ramp. After it has descended 2 vertical meters, its speed is square root of 65 m/s. What is its acceleration at this moment (in polar form and ij format)?

The diagram coupled with this question is simply looks like the mass is traveling on top of a rectangle with a quarter circle attached to it, such that the radius of this quarter circle (90 degrees) is the aforementioned height of 10m. When the mass has descended 2 meters, it is on the curve of the quarter circle.
Acceleration of gravity is assumed to be 10m/s^2

Homework Equations

mgsinθ?
F=ma?
Pythagorean Theorem?

The Attempt at a Solution

Perhaps try to find out the acceleration components of the mass? But how to do that...

 

[dwangus]

Essentially, the diagram looks like the reverse graph of square root of x function, except it is flat and perfectly curved like a circle

 

[rcgldr]

m g sin(θ) will give the component of acceleration due to gravity parallel to the surface of the ramp at that point. There's also the centripetal acceleration which is perpendicular to the surface of the ramp at that point. This requires another relevant equation. I'm not sure if you're supposed to figure out the relevant equations or if they are given to you. I'm assuming that the object's trajectory has not left the ramp in which case the object would be in free fall.

 

[dwangus]

I don't know how to calculate that; that's what I'm asking you guys LOL
Yes, its trajectory has not left the ramp yet.

 

[rcgldr]

In this case the relevant equation for centripetal acceleration is v² / r.

 

[dwangus]

But the real problem is how to find out the angle...

 

[rcgldr]

But the real problem is how to find out the angle...

You know the radius is 10 m and the object has descended 2 m. The object is 8 m above the bottom of the 1/4 circle. You should be able to determine the angle from this information.

 

[dwangus]

hm... but which angle am I exactly looking for?
I'm sorry, but I'm a beginner at all this...

 

[rcgldr]

hm... but which angle am I exactly looking for?
I'm sorry, but I'm a beginner at all this...

Is the circular ramp on the left or on the right of the flat surface? Assuming it's on the right, then θ at the top of the 1/4 circle is π / 2 radians or 90 degrees, and at the bottom of the 1/4 circle it's 0 radians or degrees. It would probably be best to have the origin at the inner corner of the 1/4 circle, so that the top of the 1/4 circle would correspond to {x, y} = {0, 10}, and the bottom right corner of the 1/4 circle would correspond to {x, y} = {10, 0}. This would mean that the small mass is on the circle at {x, 8}, and you're supposed to figure out what x is. In this case, the acceleration due to gravity is g cos(θ), tangent to the circle.

I used paint to create an image of this, see attachment.