Question

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?

Answer 1

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

Answer 2

Answer: 8.62 meters

Step-by-step explanation:

Given: The height of the rock, in meters, is given by the function $f(x)=-4.9x^2+17$ , where x is the number of seconds after Noelle releases her rock.

The height of Cesar’s rock, in meters, is given by the function $g(x)=-4.9x^2+13x$ , where x is the number of seconds after he releases his rock.

The moment when the rocks are at the same height  then f(x)= g(x)

$\Rightarrow-4.9x^2+17=-4.9x^2+13x\\\\\text{Add }-4.9x^2\text{ ion both sides, we get}\\\\\Rightarrow\ 17=13x\\\\\Rightarrow\ x=\frac{17}{13}\\\\\Rightarrow\ x=1.3076$

To calculate height put x in first equation, we get

$-4.9(1.3076)^2+17=8.62189\approx8.62$

Hence, the height = 8.62 meters