Answer:
No, he will not make it.
Explanation:
The equations for the position of the burglar during the jump are as follows:
r = (x0 + v0x · t, y0 + 1/2 · g · t²)
Where:
r = position vector of the burglar at time t
x0 = initial horizontal position
v0x = initial horizontal velocity
t = time
y0 = initial vertical position
g = acceleration due to gravity
When the burglar reaches the rooftop of the lower building, his vector position will be "r final" (see the attached figure), taking as the center of the frame of reference the jumping point. As you can see in the figure, the vector "r final" is:
r final = (8.0 m, -3.0 m)
The x-component of the vector "r final" can be calculated using the equation of the vector r, above:
x = x0 + v0x · t (x0 = 0)
8.0 m = v0x · t
In the same way with the y-component:
y = y0 + 1/2 · g · t² (y0 = 0)
-3.0 m = -1/2 · 9.8 m/s² · t²
We can calculate the horizontal velocity since we know that the burglar can run 100 m in 10,8 s. Then, his velocity will be:
v = x/t
Where: v = velocity, x = position, t = time.
v = 100 m / 10.8 s = 9.26 m/s
Now, we can calculate the time of flight of the burglar with the equation for the x-component of the vector position.
8.0 m = v0x · t
8.0 m = 9.26 m/s · t
t = 8.0 m / 9.26 m/s
t = 0.86 s
Now, let´s see what is the y-component of the vector position at that time:
y = 1/2 · g · t²
y = 1/2 · (-9.8 m/s²) · (0.86 s)²
y = -3.62 m
See in the figure the vector "r real" that will be the position of the burglar if he jumps running at that velocity. His position will be r = (8.0m, -3.62 m). He will miss the edge of the other roof by 0.62 m.
