Question

using an equation to make a prediction
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

We have the equation \( 120=-5x^{2}+250 \).

Step2: Rearrange the equation

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

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. Since \( x\) represents time (non - negative), \( x=\sqrt{26}\approx5\) (because \( 5^{2}=25\) and \( 6^{2} = 36\), and 26 is closer to 25).

Answer:

5 seconds