a professor uses a video camera to record the motion of an object falling from a height of 250 meters. the…

a professor uses a video camera to record the motion of an object falling from a height of 250 meters. the function f(x)= -5x² + 250 can be used to represent the approximate height of the object off the ground after x seconds. which is the best estimate for the amount of time elapsed when the object is 120 meters off the ground? 4 seconds 5 seconds 6 seconds 7 seconds

a professor uses a video camera to record the motion of an object falling from a height of 250 meters. the function f(x)= -5x² + 250 can be used to represent the approximate height of the object off the ground after x seconds. which is the best estimate for the amount of time elapsed when the object is 120 meters off the ground? 4 seconds 5 seconds 6 seconds 7 seconds

Answer

Explanation:

Step1: Set up the equation

We are given $f(x)= - 5x^{2}+250$ and we want to find $x$ when $f(x) = 120$. So we set up the equation $-5x^{2}+250 = 120$.

Step2: Rearrange the equation

Subtract 250 from both sides: $-5x^{2}=120 - 250=-130$. Then divide both sides by - 5, we get $x^{2}=\frac{-130}{-5}=26$.

Step3: Solve for x

Take the square - root of both sides. Since $x$ represents time, we consider the positive square root. So $x=\sqrt{26}\approx5.1$.

Answer:

5 seconds