during a building project, a brick is dropped from a height of 1,296 ft. if the equation for height as a…

during a building project, a brick is dropped from a height of 1,296 ft. if the equation for height as a function of time is h(t) = -16t² + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the brick to hit the ground? ? seconds

during a building project, a brick is dropped from a height of 1,296 ft. if the equation for height as a function of time is h(t) = -16t² + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the brick to hit the ground? ? seconds

Answer

Explanation:

Step1: Set up the equation

When the brick hits the ground, $h(t)=0$. The initial height is $1296$ ft, so the equation becomes $0=-16t^{2}+1296$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=1296$.

Step3: Solve for $t^{2}$

Divide both sides by $16$: $t^{2}=\frac{1296}{16} = 81$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t=\sqrt{81}=9$.

Answer:

9