A spy in a speed boat is being chased down a
river by government officials in a faster craft.
Just as the officials’ boat pulls up next to the
spy’s boat, both boats reach the edge of a 5.4
m waterfall. The spy’s speed is 16 m/s and
the officials’ speed is 24 m/s.
How far apart will the two vessels be when
they land below the waterfall? The acceleration of gravity is 9.81 m/s
the real question is how long to fall 5.4 meters
the easy way is to say potential energy at top = kinetic energy at bottom to find speed at bottom
(1/2) m Vb^2 = m g h
Vb = sqrt(2 g h) = sqrt (2*9.81*5.4) = 10.3 m/s at bottom
since v is linear with distance the average speed = (10.3 - 0) /2
= 5.15 m/s
so time = 5.4 meters / 5.15 meters/s = 1.05 seconds
distance between = (24 - 16)(1.05)