Incline plane problem - acceleration, time, and velocity

AI Thread Summary
The discussion centers on calculating the acceleration due to gravity on an incline plane, specifically addressing both parallel and perpendicular components. The proposed formulas for these components are parallel = 9.8sinθ and perpendicular = 9.8cosθ. A specific example using a 20-degree incline indicates that an object traveling 2 meters down would take 1.09 seconds to reach the bottom, with a calculated height of 0.684 meters above ground. It is noted that the time to drop vertically from the same height is shorter than sliding down the incline, yet both paths yield the same final velocity. The conclusion suggests that the initial calculations may be fundamentally incorrect, particularly regarding the relationship between angle and acceleration.
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Just need someone to check if this is right.

This question=frictionless, freefall, etc.

We have an incline plane. Determine the amount of acceleration due to gravity both parallel and perpendicular to the incline.
Would the answer be: parallel=9.8sinθ and perpendicular=9.8cosθ

Okay, let's say we have an inclined plane regardless of the angle, let's just make it 20 degree for instance.

The distance an object have to travel is 2m down the incline.


It would take the object 1.09 seconds to reach the bottom of the incline.

So based on this, the height above ground the object is currently at is sin20=h/2. h=.684 m.

1. The time it takes the object to drop vertically at the same height as the starting position of the object on the incline plane is comparably shorter than it would take the object to slide down the incline.

2. Both their final velocity are the same.

Make a predictive statement about the path of dependence of accelerations due to gravity.

Acceleration increases as the angle increase up to a maximum of 2 m/s^2 at 90°.
 
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It looks to me that every part is, in some important way, incorrect.
 
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