Page 66 #39 (The monkey question)

Analyzing the monkey falling straight down..................

To find the initial position (start position) of the monkey falling you can assume no acceleration due to gravity for the projectile and then the height the projectile lands at this start position.

Therefore but since acceleration will be zero for this part then

Now for the monkey falling since the initial velocity is zero.

  now remember above we proved that the initial position for the monkey was

Therefore for the monkey

Analyzing the path of the dart projectile.........

but therefore       

Therefore both final positions are the same