Question

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? 4 seconds 5 seconds 6 seconds 7 seconds

Explanation:

Step1: Substitute \( f(x) = 120 \) into the function

Given \( f(x)=-5x^{2}+250 \), when \( f(x) = 120 \), we have the equation \( 120=-5x^{2}+250 \).

Step2: Rearrange the equation

Subtract 250 from both sides: \( 120 - 250=-5x^{2} \), which simplifies to \( - 130=-5x^{2} \).

Step3: Solve for \( x^{2} \)

Divide both sides by - 5: \( x^{2}=\frac{-130}{-5}=26 \).

Step4: Solve for \( x \)

Take the square root of both sides: \( x=\sqrt{26}\approx5.1 \) (we ignore the negative root since time \( x\geq0 \)).

Answer:

5 seconds (since \( 5.1\approx5 \) among the given options)