Answer:
The distance between the ships changing at 5 PM is 21.355 knots
Step-by-step explanation:
let x = distance traveled by ship A
y = distance traveled by ship B
Let z be the distance between Ship A and Ship B
Ship A is sailing west at 16 knots and ship B is sailing north at 15 knots.
Refer the attached figure
x=50+16t
y = 15t
At 5 Pm
x=50+16(5)=130
y = 15(5)=75
We will use Pythagoras theorem
[tex]z^2=x^2+y^2[/tex]
At 7 pm [tex]z = \sqrt{(130)^2+(75)^2}=150.08[/tex]
[tex]z^2=(50+16t)^2+(15t)^2[/tex]
Differentiating both sides
[tex]2z \frac{dz}{dt}=2(50+16t)(16)+2(15t)(15)\\ \frac{dz}{dt}=\frac{(50+16t)(16)+(15t)(15)}{z}\\ \frac{dz}{dt}=\frac{(50+16(5))(16)+(15(5))(15)}{150.08}\\ \frac{dz}{dt}=21.355[/tex]
Hence The distance between the ships changing at 5 PM is 21.355 knots
