Question

an object is dropped from a bridge and allowed to freefall to the ground. the height of the object over time can be modeled using h(t)=144-16t². how many seconds will it take the object to reach the ground? 2 seconds 3 seconds 9 seconds 16 seconds

Explanation:

Step1: Set height to 0

When the object reaches the ground, \( h(t) = 0 \). So we set \( 144 - 16t^2 = 0 \).

Step2: Solve for t

First, add \( 16t^2 \) to both sides: \( 16t^2 = 144 \). Then divide both sides by 16: \( t^2=\frac{144}{16}=9 \). Take the square root of both sides (we consider positive t since time can't be negative): \( t = \sqrt{9}=3 \).

Answer:

3 seconds (corresponding to the option "3 seconds")