How Does the Angle of Inclination Change as a Skier Descends a Hill?

[Temper888]

Hey Guys,

I was doing physics questions. It was written that in the absence of friction, the acceleration of any object sliding down an inclined plane is given by:a=gsinθ. As the skier skis down the curved hill, the angle of inclination is increasing, so the acceleration of the skier is increasing. What I cannot figure out is how to know when the angle of inclination is increasing. For instance, I thought angle of inclination should increase while going up an incline. Could you please say me if there is a method of figuring out how a certain way(up or down) the incline leads to an increase or decrease in angle of inclination?

Thanks

 

[Vorde]

It would make sense that the angle is question is the angle between the angle of the hill and a line parallel to the ground at the height you started at.

 

[NascentOxygen]

As the skier skis down the curved hill, the angle of inclination is increasing, so the acceleration of the skier is increasing.

This is meaningless without reference to a diagram. Because every hill has a region where incline increases, and a region where it decreases. So if you didn't understand before reading this, you will be none the wiser after reading it.

What I cannot figure out is how to know when the angle of inclination is increasing.

Draw a tangent to the curve at your point of interest, let's call that point A. If the tangent at point A is more vertical than that at another point, then point A is on a steeper incline. If it's on a steeper incline then it will take more effort to climb up, but will be more thrilling to slide down.

For instance, I thought angle of inclination should increase while going up an incline.

Meaningless, unless the profile of your hill asymptotically approaches the vertical and has a height of infinity.

A typical rounded weathered hill is steepest about halfway up, that's where inclination is greatest. Above and below this inclination steadily decreases, and eventually it levels out to zero inclination at the flat summit and also away from the base.

 

[cupid.callin]

Someone please draw a hill for reference ...

I really am getting confused with my mind and NascentOxygen's post