Question

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? enter your answer, rounded to the nearest tenth of a meter, in the box.

Answer 1

Step-by-step explanation:

To find the height at which the rocks are at the same height, we need to set the two height functions equal to each other and solve for x.

f(x) = g(x)

-4.9x^2 + 17 = -4.9x^2 + 13x

Simplifying the equation, we have:

0 = 13x - 17

Rearranging the equation:

13x = 17

Dividing both sides by 13:

x = 17/13

Now, we can substitute this value of x back into either f(x) or g(x) to find the height at that moment.

Using f(x) = -4.9x^2 + 17:

f(17/13) = -4.9(17/13)^2 + 17

Calculating this value, we get:

f(17/13) ≈ 16.5

Therefore, at the moment when the rocks are at the same height, the height is approximately 16.5 meters (rounded to the nearest tenth of a meter).