Calc
posted by Pierre .
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

First draw a right triangle
Let side y be the distance by B in the time after noon this will be 15*7
Let side x be the distance traveled in total by A this will be 30+ (16*7)
so you have y=105 and x=142
Ship B is sailing at 15 knots, this is the rate it is changing, so it is also written as dy/dt=15
Ship A is sailing at 16 knots so this is written as dx/dt=16
you need the distance formula, write is as
h^2=x^2 + y^2
h is the hypotenuse of your triangle, or the distance between the two points
At this point there are two different approaches
APPROACH 1
h^2=x^2 + y^2 is the same as
h=(x^2+ y^2)^(1/2)
Find dh/dt
dh/dt=(1/2)(x^2+ y^2)^(1/2) (2x dx/dt + 2y dy/dt)
dh/dt=(2x dx/dt + 2y dy/dt)/ [2(x^2+ y^2)^(1/2)]
plug in:
y=105
x=142
dx/dt=16
dy/dt=15
dh/dt=___

APPROACH 2
h^2=x^2 + y^2
plug in your x and y and solve for h
h=(x^2+ y^2)^(1/2)
h=[(142)^2 + (105)^2]^(1/2)
h=(31189)^(1/2)
using h^2=x^2 + y^2 find dh/dt
2h dh/dt= 2x dx/dt + 2y dy/dt
solve for dh/dt by plugging in:
h=(31189)^(1/2)
y=105
x=142
dx/dt=16
dy/dt=15 
33.95230566

The area of a circular sinkhole increases at a rate of 420 square yards per day. How fast is the radius of the sinkhole growing when its radius is 50 yards?

Helicopters.
Respond to this Question
Similar Questions

Calc
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 20 knots and ship B is sailing north at 20 knots. How fast (in knots) is the distance between the ships changing at 4 PM? 
CALCULUS
At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 5 PM? 
Calc
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship B is sailing north at 18 knots. How fast (in knots) is the distance between the ships changing at 6 PM? 
Calc
At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 19 knots and ship B is sailing north at 20 knots. How fast (in knots) is the distance between the ships changing at 7 PM? 
calculus
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 25 knots. How fast (in knots) is the distance between the ships changing at 6 PM? 
calculus
At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 3 PM? 
calculus
At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 3 PM? 
calculus
At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 3 PM? 
Calculus
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 19 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 3 PM? 
calc
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 6 PM?