Question

Two ships leave port at 9:00 am, one sailing south at a rate of 16 mph and the other sailing west at a rate of 20 mph. If

t denotes the time (in hours) after 9:00 am, express the distance d between the ships as a function of t.?
A) d(t) =√16t²+20t
B) d(t) = √16²-20t²
C) d(t) =√16² +20².t
D) d(t) =√16² -20² .t

Answer 1

The distance between the two ships can be calculated using the Pythagorean theorem, resulting in the function d(t) = 4t√41.

Step-by-step explanation:

The distance between the two ships can be calculated using the Pythagorean theorem, as they are moving at right angles to each other.

The distance the first ship travels is given by d1 = 16t, and the distance the second ship travels is given by d2 = 20t.

Using the Pythagorean theorem, the distance between the ships is d = √(d1^2 + d2^2) = √(16^2t^2 + 20^2t^2) = √(256t^2 + 400t^2) = √(656t^2) = 4t√41.

Therefore, the function that represents the distance between the ships as a function of time is d(t) = 4t√41.