Question

a pebble falls off of a cliff at a height of 784 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 pebble to hit the ground? ? seconds

Explanation:

Step1: Set height to 0

When the pebble hits the ground, $h(t)=0$. The initial height is 784 ft, so the equation becomes $0 = - 16t^{2}+784$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=784$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{784}{16}=49$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t=\sqrt{49}=7$.

Answer:

7