Calculating the velocity of an object down a varied slope inclined plane

  • Thread starter dougk
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  • #1
dougk
An object starts at a height of 5m. The initial incline is 63.4 deg. After moving 2m in the x direction, the incline decreases to 7.125 deg and the motion continues for an additional 8m in the x direction. What is the total time for the object to complete the path?


Homework Equations


The initial move downward is 4m in the y and 2m in the x direction. The second move is 1m in the y and 8m in the x direction.

The Attempt at a Solution


Tried to solve it separating the moves and adding the time together.
 

Answers and Replies

  • #2
34,677
10,818
Tried to solve it separating the moves and adding the time together.
That is a good approach. Where is the problem?
 
  • #3
dougk
We solved for the time in the x direction and the y direction to make sure they matched. For the first leg, they did, for the second leg they didn't.

I took my kids to the math musuem in the city last week and we saw an exhibit that highlighted the fastest way down a gravitational field. We're trying to work out a simpler method by using segments.

Thanks,

Doug
 
  • #4
haruspex
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We solved for the time in the x direction and the y direction to make sure they matched. For the first leg, they did, for the second leg they didn't.

I took my kids to the math musuem in the city last week and we saw an exhibit that highlighted the fastest way down a gravitational field. We're trying to work out a simpler method by using segments.

Thanks,

Doug
Please post your working (or there's no way to tell where you went wrong).
 
  • #5
34,677
10,818
I took my kids to the math musuem in the city last week and we saw an exhibit that highlighted the fastest way down a gravitational field. We're trying to work out a simpler method by using segments.
No finite number of segments will give the optimum. Adding more and more segments in the right way will always improve the time - with the ideal curve as limiting case.
 

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