A 80 kg stuntman falls of a 20m platform ,falls for 18m and lands on a 2m deep foam mat what is the minimum upward force the mat must exert to keep him from hitting the ground

(In the following, by x^2, I mean square of x)

Suppose he hits the mat with velocity = v
Acceleration a = g, u = initial velocity = 0, s = distance = 18

You can find v by using the formula: v^2 - u^2 = 2as (here v^2 = square of v)
Hence v^2 = 36 g

You have found v, the velocity when he touches the mat

Suppose upward acceleration by mat is = b
Downward acceleration = g
Net downward acceleration = g - b

Final velocity = 0, initial velocity = v (caluculated above), distance = 2

Formula: v^2 - u^2 = 2 x acceleration x distance
0 - v^2 = 2(g - b)2
v^2 = 4(b - g)
b - g = v^2/4
b = g + v^2/4

Substitute the values of g and v.

So you have found the acceleration b applied by mat
Now you can find Force applied by mat = mass x acceleration = 80b

Let me know if any step is not clear