Thread: Force on one face of a right triangle

1. Force on one face of a right triangle

Got no idea how to solve this problem. All I know is that it's related to differential calculus and most definitely use vectors.

Find the force on one face of a right triangle of sides 4 meters and altitude of 3 meters. The altitude is submerged vertically with the 4 meter side in the surface.

Can anyone show me how ?

2. The selections by the way are

a. 58.86 kNewton
b. 53.22 kNewton
c. 62.64 kNewton
d. 66.27 kNewton

3. Pressure of water at depth h is:
$P(h) = \rho g h$.

Where $\rho$ is the density of water, and g the acceleration due to gravity.

Total force on triangle is then

$\displaystyle \int_A P(h) dA = \int_A (\rho g h) dA = \int_0^3 \int_0^{4 - \frac{4}{3}h} (\rho g h) dw dh$

Where dw is along the width of the triangle.