Your friend is writing a crime drama and wants your input on the credibility of a plot point. a burglar is running as fast as he can on the flat roof of a building, trying to escape the police. as he approaches the ledge, he spots another flat rooftop that is 8.0 m across the alley and 3.0 m lower than the building on which he is currently running. earlier in the story, it was revealed that the burglar can run the 100-m dash in 10.8 s. can he make the leap when moving at full speed?

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.

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