Distance Between Two Cargo Ships Ship A leaves port sailing north at a speed of 35 mph. A half hour later, Ship B leaves the same port sailing east at a speed of 30 mph.

Question

Let t (in hours) denote the time ship B has been at sea.

(a)

Find an expression in terms of t giving the distance D between the two cargo ships.

d(t)=

Use the expression obtained in part (a) to find the distance (in miles) between the two cargo ships 2 hr after Ship A has left port. (Round your answer two decimal places.)

 mi

Answer 1

from origin to ship A = 35(t+1/2)

from origin to ship B = 30t

D= distance between them at time t

D^2 = (35t+35/2)^2 + (30t)^2

D = sqrD^2

in 2 hours, D(2) = square root of (70+35/2)^2 + 60^2 = sqr(7656.25 + 3600) = sqr11256.25=106.10 miles

D is the hypotenuse of a right triangle with 2 sides, 30t and (35t+35/2)