Arescue line is to be thrown horizontally from the bridge of a cruise ship at 40.0 m above sea level to a life boat 50.0 m away with what horizontal speed should the rescue line be thrown?

There is a 40m drop from the bridge, so we can work out the time of the vertical component first (how long it will take to reach the water) 

do this by using a SUVAT equation s=ut+0.5at^2
this rearranges to t= sqrt(2s/a)
- note that u has been removed since there is no initial velocity.
 
sqrt((2*40)/9.81)= 2.86 seconds 

this means that the horizontal component of 50m has so be covered in 2.86s 
and speed = distance/ time 

50m/2.86s=17.48ms^-1

the line has to be thrown at 17.48ms^-1 or more to reach the life boat.