Answer:
18 miles east; 24 mph east
Explanation:
In order to find how far east of Wilmington is the ship after 1 hour, we just need to substitute t = 1 into the formula of the position.
The equation of the position is
[tex]s(t) = 12 t^2 +6[/tex]
where t is the time. Substituting t = 1,
[tex]s(1) = 12 (1)^2 + 6 = 12+6 = 18 mi[/tex]
So, the ship is 18 miles east of Wilmington.
To find the velocity of the boat, we just need to calculate the derivative of the position, so
[tex]v(t) = s'(t) = 24 t[/tex]
And by substituting t = 1, we find the velocity after 1 hour:
[tex]v(1) = 24 (1) = 24 mph[/tex]
And the direction is east.
