Question

1.From What height is the coin thrown1a. At what time does the coin reach the ground

Answer 1

1a) 960 ft

1b) 10 seconds

Step-by-step explanation:

`\begin{gathered} 1a)\text{ }h(t)=-16t^2\text{ + 64t + 960} \\ Since\text{ t = 0 when the coin was thrown, we'll replace t with 0 in the function above} \\ h(t)=-16(0)^2\text{ + 64(0) + 960} \end{gathered}`
`\begin{gathered} h(t)\text{ = 0 + 0 + 960} \\ h(t)\text{ = 960 f}eet \\ \text{Hence, the coin was thrown at height 960 ft} \end{gathered}`
`\begin{gathered} 1b)\text{ When the coin reach the ground, h(t) = 0 ft} \\ We\text{ would replace h(t) with 0 in the given function} \end{gathered}`
`\begin{gathered} 0=-16t^2\text{ + 64t + 960} \\ \text{The factorised function was given in the question.} \\ We\text{ would use that:} \\ 0\text{ = -16(t - 10)(t + 6) (divide both sides by -16)} \\ 0\text{ = (t - 10)(t + 6)} \\ t\text{ - 10 = 0 or t + 6 = 0} \\ t\text{ = 10 or t = }-6 \end{gathered}`
`\begin{gathered} \text{Since time cannot be negative, t = 10} \\ \text{The coin reaches the ground at 1}0\text{ seconds} \end{gathered}`