Noelle stands at the edge of a cliff and drops a rock. The height of the rock, in meters, is given by the function f(x)=−4.9x2+17 , where x is the number of seconds after Noelle releases her rock.Cesar, who is standing nearby on the ground, throws a rock straight up in the air. The height of Cesar’s rock, in meters, is given by the function g(x)=−4.9x2+13x , where x is the number of seconds after he releases his rock.There is a moment when the rocks are at the same height. What is this height?

For this case what we must do is to equal both functions at the moment in which it is to find the result.
 We have then:
 f (x) = g (x)
 -4.9x2 + 17 = -4.9x2 + 13x
 Clearing x we have:
 17 = 13x
 x = 17/13
 x = 1.31 s
 Then, to find the height, with respect to the floor we have:
 g (1.31) = - 4.9 * (1.31) ^ 2 + 13 * (1.31)
 g (1.31) = 8.62
 Answer:
 The height with respect to the ground is:
 8.62 m