Length- Supports

[Guest]

A slide of uniform grade is to be constructed on a level surface and is to have 10 supports with equal distances between the supports.

Length of longest support- 42.5 feet
Length of shortest support- 2 feet

Calculate length of each support.

[Guest]

Gradient of slide is 4.5 feet of rise per support.

Sn = 4.5(n-1) + 2

S1 is 4.5 x 0 = 2 feet
S2 is 4.5 x 1 =
S3
etc....
..
..
..

S10 is 4.5 x 9 + 2 = 42.5

[Guest]

Please explain your solution in more detail. I am not clear.

Thanks.

[Guest]

"A slide of uniform grade"........I assume this is typing error and means.....uniform gradient......that is a straight line at an angle which is constant. There are 10 supports so that means 9 spaces or if it was steps it would be 9 steps.
The slope or gradient of the slide is the change in height per step or per support.

The total change in height is 42.5 - 2.0 = 40.5......divide this by 9 and we get 4.5 per support.
That means each support is 4.5 higher than the previous one and the first one is 2.0 high.
So the 2nd is 6.5 and the 3rd is 11.0 and the 4th is 15.5 and the 5th is 20.0 and the 6th is 24.5 and the 7th is 29.0 and the 8th is 33.5 and the 9th is 38.0 and the last the 10th is 42.5. ......10 supports and 9 spaces or steps.

The formula just makes it a bit more mathematical......... n is the number of the support Sn we are calculating the height.
It is an arithmetic series...... the common difference is 4.5 the first value is 2.0........Sn is the value of the nth term....

Or.... of the formula for a straight line graph......y = Mx + C ....... Sn = 4.5(n-1) + 2

Sn = 4.5(n-1) + 2

S1 is 4.5 x 0 + 2 = 2 feet
S2 is 4.5 x 1 + 2 = 6.5 feet
S3 is 4.5 x 2 + 2 = 11.0 feet
and so on until.....
S10 is 4.5 x 9 + 2 = 42.5 feet

[Guest]

"A slide of uniform grade"

That is what the problem states.

I understand the solution now. Thanks again.

[Guest]

A question:

Can approximate length of the slide be calculated from total length of the supports if placed end to end and due to equal spacing between supports ?

[Guest]

The length of the slide (either horizontal or sloping length) depends on the spacing of the supports, not the length of the supports. Sloping length = square root ( (9 x the spacing)^2 + (40.5)^2).

Its just Pythagoras and a right angled triangle.