calculus
posted by Anya .
Boat A leaves the dock at 12pm heading due South at a constant speed of 20 km/h.
Meanwhile, at 12pm Boat B, a pirate ship, is 15 km due West of the dock where boat
A started, and is sailing due East at a constant speed of 15 km/h. If the pirates get
within 10 km of another boat, they will spot it and eventually capture it. Is Boat A
in danger of getting captured by the pirates on Boat B?

calculus 
Reiny
Make a diagram showing the ships at t hours after 12:00 pm.
Let D be the position of the dock and A and B the position of the boats.
then DA = 20t km
and BD = (1515t) km
AB^2 = (20t)^2 + (1515t)^2
let's find the minimum distance AB
2AB d(AB)/dt = 800t + 2(1515t)(15)
= 0 for a minimum of AD
800t  30(1515t) = 0
800t  450 + 450t =
t = 450/1250
t = .36 hours
when t = .36
(AB)^2 = 51.84 + 92.16
AB = √144
= 12
Since they have to be within 10 km to be seen, they are ok.
Respond to this Question
Similar Questions

Physics
A speed boat at rest begins to move in a straight line from a dock. The boat has a constant acceleration of +3.0 m/s squared. Attached to the dock is a siren that is producing a 755 Hz tone. If the air temperature is 20 degrees C, … 
Calculus
At 2:00PM boat X is heading due west at 15mph towards a dock that is exactly 15 miles away. At the same time boat Y leaves the dock traveling due north at a speed of 20mph. At what time will the boats be closest together? 
calculus
a boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 pm. at what time were the two boats closest together 
math
a boat leaves a dock at 2:00pm ,heading west at 15 km/h. another boat heads south at 12km/hand reaches the same dock at 3:00 pm, when were the boats were closest to each other.? 
Calculus Practice Problems
A boat is pulled into a dock by a rope attached to the bow (front end) of the boat and passing through a pulley on the dock that is 4 m higher than the bow of the boat. If the rope is pulled in at a rate of 3 m/s, at what speed is … 
Calculus (math)
A boat leaves a dock at 2:00 P.M. and travels due south at a speed of 15 km/h. Another boat has been heading due east at 20 km/h and reaches the same dock at 3:00 P.M. How many minutes past 2:00 P.M. were the boats closest together? 
Calculus (math)
A boat leaves a dock at 2:00 P.M. and travels due south at a speed of 15 km/h. Another boat has been heading due east at 20 km/h and reaches the same dock at 3:00 P.M. How many minutes past 2:00 P.M. were the boats closest together? 
calc
A boat leaves a dock at 3:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 4:00 PM. How many minutes after 3:00 PM were the two boats closest together? 
Precalculas
Boat A leaves a dock headed due east at 1:00 PM traveling at a speed of 16 mi/hr. At 2:00 PM, Boat B leaves the same dock traveling due north at a speed of 18 mi/hr. Find an equation that represents the distance d in miles between … 
Precalc
Boat A leaves a dock headed due east at 1:00PM traveling at a speed of 13 mi/hr. At 2:00PM, Boat B leaves the same dock traveling due north at a speed of 20 mi/hr. Find an equation that represents the distance d in miles between the …