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?

Question

Mathematics

Addison Swanson

22 April, 03:37

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?

+1

Answers (1)

Know the Answer?

Frida · 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