Question

The function h defined by h(t)=(49+4.9t)(10−t) models the height, in meters, of an object t seconds after it is dropped from a helicopter.Find or approximate the time when the object hits the ground. Explain or show your reasoning.From what height is the object dropped? Explain or show your reasoning.

Answer 1

Step 1

Given;

$h(t)=(49+4.9t)(10-t)$

Step 2

Find or approximate the time when the object hits the ground.

$\begin{gathered} we\text{ set h\lparen t\rparen=0} \\ 0=(49+4.9t)(10-t) \\ 49+4.9t=0\quad \mathrm{or}\quad \:10-t=0 \\ t=-10,\:t=10 \\ Time\text{ cannot be negative hence t=10seconds} \end{gathered}$

Step 3

From what height is the object dropped?

$\begin{gathered} h(t)=(49+4.9t)(10-t) \\ h(t)=490-4.9t^2 \end{gathered}$

Considering the equation above and the graph below, we can deduce that;

$The\text{ ball was dropped from 490meters since the object was just dropped}$

Answer to the second part- 490 meters