A man standing at the top of a building kicks a small rock of massm. The height of the building ishand initialvelocity of the rock after the kick is~v =< v,0,0>. Assume no air resistance and let g be the magnitude of the acceleration due to gravity. a. Find the time taken by the rock to hit the ground.
b. How far away from the building did the rock travel before hitting the ground?
c. Determine the magnitude of velocity of the rock before hitting the ground.

Centrapedial force is the answer

You need to be more specific.  i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time,  then constant velocity is a straight line . . i.e. a line that has  constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant  velocity is a piece of line that lies on the x-axis . . it's value is zero. 

At maximum height, kinetic energy is converted in potential energy  formula: at max height, ke = ½ * 0.27kg * (16m/s) ² = 34.56 j  so the remaining pe = (41.70 – 34.56)= 7.14 j = 0.27 kg * 9.8m/s² * h  = (9.8/7.14 * 0.27)so max height h = 5.08 or 5 m