Building Sand Castle Walls: Force vs. Exponential

[russell16]

I am at a beach with my family and we were building a sand castle and we wanted to build a wall around it so it would last longer against high tide. I said to my cousins that the wall should be slanted in order to decrease the force of the water instead of being flat because then the wall would take the full force and it would not be distributed as well. And i used the term exponentially because i knew it was greater than a proportional difference and i wanted it done my way. another cousin said that he thinks it wouldn't be exponentional. he does agree that would better distribute the force but thinnks it would be a proportion. I just decided for sake of arguing to keep my side and say exponential. If anyone can provide equational proof that force of water flowing on to a slanted surface is exponential or proportional it would be apprieciated.

 

[HallsofIvy]

The force hitting a wall does not depend at all upon its being slanted. What is true is that a slanted wall has a larger base than a non-slanted wall of the same amount of material and so resists that force better.