Answer:
4 seconds
Step-by-step explanation:
Given equation:
[tex]y=256-16x^2[/tex]
where:
- y = The height of the penny (in feet).
- x = The time since the penny was dropped (in seconds).
The penny reaches the ground when the height is zero, so when y = 0.
Substitute y = 0 into the given equation and solve for x:
[tex]\begin{aligned}y&=256-16x^2\\y=0 \implies 0&=256-16x^2\\0+16x^2&=256-16x^2+16x^2\\16x^2&=256\\\dfrac{16x^2}{16}&=\dfrac{256}{16}\\x^2&=16\\\sqrt{x^2}&=\sqrt{16}\\x&=\pm4\end{aligned}[/tex]
As time is positive, x = 4 only.
Therefore, it takes 4 seconds for the penny to reach the ground.
