Step-by-step explanation:
The problem statement says λ<1. If this is true, then the cannonball is slower than the boat, and it will never reach the boat. So I assume it's actually λ>1.
If we say t is the amount of time, then the boat travels south a distance of ut, and the cannonball travels a distance of λut.
v = λut
ut = v/λ
Using Pythagorean theorem:
d² + (ut)² > v²
d² + (v/λ)² > v²
λ²d² + v² > λ²v²
λ²d² > (λ² − 1) v²
λ² / (λ² − 1) > (v/d)²
