Who Will Reach the Bottom of the Hill First?

[Shaunzio]

If there are 3 people going down a hill at different angles but still starting at the same point, who will reach the bottom of the hill first? The first person is going down a slope of 30 degrees. The second person is going down a slope of 20 degrees. And the last person is going down a slope of 10 degrees. Neglect friction.
F=maWell i thought that there was not enough information because you do not know the mass, but since it said to neglect friction then the person on the 30 degree would just be accelerating at gravity. Someone please tell me if I'm rite.

 

[Dr.D]

Do you know what a rite is? You should look it up.

Set up the problem of a block sliding down a hill at an angle theta above the horizontal. Find out how the angle affects the transit time from the top to the bottom. Then it will be fairly straight forward to answer the original problem.

 

[Shaunzio]

sorry for my poor grammar but I still don't understand. Would the person at the 30 degree hill reach first since the angle is greater and therefore giving a greater velocity?

 

[Dr.D]

Did you read the second paragraph?

 

[Shaunzio]

Ok...but I don't know how the angle affects the transit time from the top to the bottom. That's why I came here. If you could tell me that would be great. Thanks.

 

[PhanthomJay]

In the absence of friction and air drag, there is only one force, acting parallel to the slope, acting on the persons: the gravitational component acting down the plane. Are you familiar with free body diagrams? Intuitively, if the slope was real small, you wouldn't expect much acceleration or speed; if the slope was steep, you'd expect a lot more acceleration and speed, since speed and acceleration are related by the kinematic equations of motion. As theta increases, the acceleration down the plane increases, and thus the speed increases, independent of the person's mass. You might want to look at this site: www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Dynamics/InclinePlanePhys.html[/URL] . (Scroll down to 'Frictionless incline with no applied forces'). I hope this helps to understand the situation.