Photo from Miyako city gov.

GraceKyotoTsunamiCalculate

Wall side(a) fixed 4 kilometers

Another side(b) decreasing at the rate of 0.8 kilometers per minute

Speed on land(h) increasing at a rate of 0.6 kilometers per minute.

At a certain time, side(b) is 10kilometers and the h is 2 kilometers.

What is the rate of change in the area at that instant

A(area) = \frac{a+b}{2}h

a = 4 Km, b = 10 Km, h = 2Km, t = time

\frac{db}{dt} = -0.8Km/min\frac{dh}{dt} = 0.6Km/min

\frac{dA}{dt} = \frac{d}{dt}[\frac{a+b}{2}h]

\frac{dA}{dt} = \frac{1}{2}\frac{d}{dt}[4h(t)+b(t)h(t)]

\frac{dA}{dt} = \frac{1}{2}(4\frac{dh}{dt} + \frac{db}{dt}h +b\frac{dh}{dt})

\frac{dA}{dt} = \frac{1}{2}(4\times0.6 + (-0.8\times2) + 10\times0.6) = 3.4km^2/min

def TAcalc(a,b,h,bv,hv):
    """
    a = wall side, b = another side at time t, h = tsunami length on land,
    bv = velocity of b, hv = velocity of h     usage TAcalc(a,b,h,bv,hv)
    """
    return 1/2*(a*hv + bv*h + b*hv)

TAcalc(4,10,2,-0.8,0.6)