Data 605 Week 13 Discussion

#Question 10 Chapter 4.2 A boat is being pulled into a dock at a constant rate of 30ft/min by a winch located 10􀅌 above the deck of the boat. At what rate is the boat approaching the dock when the boat is: (a) 50 feet out?

z <-50
dz_dt <- 30
z/(sqrt(z^2 - 100)) * dz_dt

## [1] 30.61862

2. 15 feet out?

z <-15
z/(sqrt(z^2 - 100)) * dz_dt

## [1] 40.24922

3. 1 foot from the dock?

z <- 1
z/(sqrt(z^2 - 100)) * dz_dt

## Warning in sqrt(z^2 - 100): NaNs produced

## [1] NaN

This doesn’t exist? (d) What happens when the length of rope pulling in the boat is less than 10 feet long?