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 $f(x)=-5x^{2}+250$ 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?\n4 seconds\n5 seconds\n6 seconds\n7 seconds

a professor uses a video camera to record the motion of an object falling from a height of 250 meters. the function $f(x)=-5x^{2}+250$ 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?\n4 seconds\n5 seconds\n6 seconds\n7 seconds

Answer

Explanation:

Step1: Set up the equation

Set $f(x)=120$, so $- 5x^{2}+250 = 120$.

Step2: Rearrange the equation

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

Step3: Solve for x

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

Answer:

5 seconds