Question

a family is 500 feet above the ground in a basket of a hot-air balloon and asending at the consistent rate shown. At the height someone actually drives a penny out of the balloon write a model for the height h of in feet of the balloon T seconds after the penny is dropped

Answer 1

Given :

initial height = 500

initial speed of the penny = 10 ft/sec

The gravity = -32 ft/s^2

So,

`\begin{gathered} h_0=500\text{ ft} \\ v_0=10\text{ ft/s} \\ a=-32\text{ ft/s\textasciicircum{}2} \\ \\ \end{gathered}`

The equation of the height will be :

`\begin{gathered} h-h_0=v_0\cdot t+0.5\cdot a\cdot t^2 \\ \\ h-500=10t-0.5\cdot32\cdot t^2 \\ \\ h=-16t^2+10t+500 \end{gathered}`