# Thread: Related Rates - Calculus Problem

1. ## Related Rates - Calculus Problem

A dam is inclinded at an angle of 30 degrees from the vertical and has the shape of an isosceles trapezoid 100 feet wide at the top and 50 ft wide at the bottom and with a slant height of 70 ft. Find the hydrostatic force on the dam when it is full of water.

*The thing that keeps fooling me is when it says 100 ft at the top and 50 at the bottom, shouldn't those numbers be reserved to make an isosceles trapezoid?

2. Originally Posted by action812
A dam is inclinded at an angle of 30 degrees from the vertical and has the shape of an isosceles trapezoid 100 feet wide at the top and 50 ft wide at the bottom and with a slant height of 70 ft. Find the hydrostatic force on the dam when it is full of water.

*The thing that keeps fooling me is when it says 100 ft at the top and 50 at the bottom, shouldn't those numbers be reserved to make an isosceles trapezoid?
narrow dimension is on the bottom ... see why?

3. Haha I'm making some silly mistakes today. So my first task would be to find the amount of water the dam is emerged in which takes a little bit of trig. Using the 30-60 triangle formula I got that the dam is emerged 60.62 ft. Correct?

4. Ok after a little work I got the force to be equal to the integral from 0 to 60.62.

Inside the integral is 62.4x(100)(60.62).

Sorry for not using the correct math notation, I'm not sure how...Is this right, am I missing a pi in there anywhere?

Using this notation I got the answer to be 695,028,142 ft/lbs. Seems a little high, can anyone confirm if my notation is correct? Thanks

5. Anyone? I leave for class soon. xx