Need some help over here!

Let the velocity of the man at the topmost point of the slope be v.Now from here projectile motion starts at an angle of 45.
So v²=900.....[as θ=45]
or, v=30.
Now along the incline decelaration=gsin45.
So u² - v²=2*gsin(45)*80√2.
or, u=50. This is the minimum required speed.

Sorry, I did not get your solution. I worked it out on my own. The answer is correct though. It IS 50 m/s.