Question

A triangle with a base of 4 m and height of 5 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 to the nearest whole number.

a) ∫0 to 5 4x dx ≈ 40

b) ∫0 to 4 5x dx ≈ 30

c) ∫0 to 5 5x dx ≈ 50

d) ∫0 to 4 4x dx ≈ 20

Answer 1

The hydrostatic force against one side of the plate can be expressed as an integral and evaluated to approximately 50 units.

Step-by-step explanation:

The hydrostatic force against one side of the plate can be expressed as an integral using the formula F = ∫(0 to h) ρgx dA, where ρ is the density of water, g is the acceleration due to gravity, h is the height of the submerged portion of the triangle, and dA is the differential area of the submerged portion. In this case, the height of the triangle is 5 m and the base is 4 m.

Using the formula and integrating, the integral would be ∫(0 to 5) 4x dx, where x represents the distance from the base of the triangle to the height.

Evaluating this integral gives us ∫(0 to 5) 4x dx = [2x^2] from 0 to 5 = 2(5^2) - 2(0^2) = 50. Therefore, the hydrostatic force against one side of the triangle is approximately 50 units.