Part-1: Mean Kid pushes Nice Kid off a dock into the water. Mean does this by pushing Nice horizontally. But, karma has finally caught up with Mean and at the same instant that Mean pushes Nice horizontally, the dock also collapses and Mean immediately begins to fall towards the water as well. (Karma isn't finished with Mean though, because only Nice knows how to swim.) Choose the correct statement.
a. Nice hits the water at the same time as Mean
b. Mean and Nice have the same speed throughout their trajectories
c. Nice hits the water first
d. Mean hits the water first
e. Mean has a greater acceleration mid-flight, than Nice in mid-flight
Part-2: Mean Kid pushes Nice Kid off a dock into the water. Mean does this by pushing Nice horizontally. But, karma has finally caught up with Mean and at the same instant that Mean pushes Nice horizontally, the dock also collapses and Mean immediately begins to fall towards the water as well. After Nice swims to shore, Karma arranges for a jelly fish to give Mean a bit of a sting. Choose the correct statement.
a. Mean and Nice hit the water with the same speed
b. Nice hits the water faster than Mean
c. Mean hits the water with a larger vertical component of speed than Nice's vertical component of speed
d. Nice hits the water slower than Mean

Since Nice is pushed horizontally, in the vertical direction, he has no initial component of velocity, due to both movements are independent each other.

Since the dock collapses, this means that in the vertical direction, the movement of Mean is exactly the same as Nice's.

The expression for the vertical displacement is given by the following equation:
[tex]\Delta y = \frac{1}{2} * g*t^{2} (1)[/tex]

So, due to the time of flight is determined by the height exclusively, and they start from the same height, we can conclude that they will hit the water at the same time.

Part-2

The speed of both kids is given by the vector sum of the vertical and horizontal components of velocity when they hit the water.

Mean falls vertically, with no component of velocity in the horizontal direction.

In the vertical direction, Nice falls with exactly the same speed, as they hit water at the same time.

However, Nice has a horizontal component of the velocity, that keeps constant during all his flight, as no external forces act in the horizontal direction.

So, the magnitude of Nice's speed must be larger than Mead's, due to the vertical components are the same, and the extra horizontal component of Nice's adds to the vertical one.