I guess the question is to find what speed the stuntman must have to jump across the gap.
He needs to launch himself at an angle of 45 degrees to make the best distance. His speed is v.
The equations are y=vtsin45-gt²/2 and x=vtcos45, where x=4m and y=0 and t is time.
Since t=0 is the start of the jump, we can divide by t to get t=2vsin45/g.
Also t=4/(vcos45). We can equate these two values for t: 2vsin45/g=4/(vcos45).
So 2v²sin45cos45=4g, or v²=4g since 2sin45cos45=sin90=1.
Using g=9.8m/s² as the acceleration of gravity, v²=39.2 and v=6.26 m/s approx. This is the minimum speed.
If the angle of launch is not 45 degrees, we have v²sin(2θ)=4g, where θ is the launch angle. The largest value for sine is 1, hence 45 degrees for the best angle. Speed has to be increased for different launch angles.