# Calc

posted by .

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.)

• Calc -

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

• Calc -

33.95230566

• Calc -

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?

• Calc -

Helicopters.

## Similar Questions

1. ### 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?
2. ### 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?
3. ### 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?
4. ### 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?
5. ### 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?
6. ### 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?
7. ### 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?
8. ### 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?
9. ### 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?
10. ### 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?

More Similar Questions