A triangle with base 2 m and height 3 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Give your answer correct to the nearest whole number.)

Check the attached

Step-by-step explanation:

The Force on one side of the pate is 58800N.

Step-by-step explanation:

The base of triangle is given as b=2m

The height of triangle is given as h=3m

Gravitational Acceleration is given as g=9.8 m/s^2

The density of water is given as ρ =1000 kg/m3

Now for a rectangular strip DE as shown in the attached figure, of width dy and length x is considered for which the area is

The area is given as

Also for this the pressure at depth y is given as

As the triangles are similar so

Now the differential force is given as

Now for the total force, the integral for 0 to h=3 m is given as

So the Force on one side of the pate is 58800N.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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