We know this is a piecewise function and we solved the first part, but we cannot figure out the other equation.

Question

A passenger ship leaves port sailing east at 16 mph. Two hours later, a cargo ship leaves the same port heading north at 12 mph.
(a) Find a function giving the distance in miles between the two ships t hr after the passenger ship leaves port.

D(t)={16t if 0<t<4
={??? if t>2

Answer 1

passenger ship east = 16 t
if t</= 2 then 16 t is the answer

if t >2
cargo ship north = 12 (t-2) (t>2 :)

d^2 = (16t)^2 + 144(t^2 -4 t + 4)
d^2 = 256 t^2 + 144 t^2 -576 t + 576

d^2 = 400 t^2 -576 t + 576
d = sqrt (400 t^2 -576 t + 576)
check, yes that is 32 miles at t = 2 :)