96 km per hour is the rate at which the space between the ships is reducing.
Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Speed is a scalar quantity since it just has a direction and no magnitude.
The ratio of distance travelled to time taken can be used to determine speed.
Ships A and B have travelled a combined distance of d.
Given that the two ships have travelled a total distance of, the two ships' distance at time t hours equals;
d(t) = √[(90 - 0)² + (10 - (-20))²]
d(t) = √(8100 + 900t²)
Let's differentiate utilising the chain rule now to determine how quickly the distance between the ships is changing;
d'(t) = [1/(2√(8100 + 900t²))] × 7200t
d'(t) = 3600t/√(8100 + 900t²)
d'(t) = 3600t/10√(81+ 9t²)
d'(t) = 360t/√(81 + 9²)
Now, at 4pm would have been 4 hours from noon. Thus, t = 4.
So;
d'(t) = (360×4)/√(81+ 9(4²))
d'(t) = 1440/√(81 + 144)
d'(t) = 1440/√225
d'(t) = 1440/15
d'(t) = 96 km/h
Hence, The rate that the distance between the ships is changing is 96 km per hour
To learn more about speed refer to:
https://brainly.com/question/6504879
#SPJ1
