Question

the function h is 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 a) find the time when the object hits the ground. explainb) from what height is the object dropped ? explain

Answer 1

The function that models the hight of an object after some time t is:

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

a) when the object hits the ground the hiht will be equal to 0 so we replace and slve for t:

$0=(49+49t)(10-t)$

and solving for t will be:

$\begin{gathered} 0=490-49t+490t-49t^2 \\ 0=10-t+10t-t^2 \\ t^2-9t-10=0 \end{gathered}$

and we solve it with the cuadratic function so:

$\begin{gathered} t=\frac{9\pm\sqrt[]{9^2-4(1)(-10)}}{2(1)} \\ t=\frac{9\pm\sqrt[]{81+40}}{2} \\ t=\frac{9\pm\sqrt[]{121}}{2} \\ t_1=\frac{9+11}{2} \\ t_1=\frac{20}{2} \\ t_1=10 \end{gathered}$

it takes 10 second to reach the ground.

b) to find the hight the object was drop we can replace t=0 that is the exact tiem whre the object was dropt so:

$\begin{gathered} h=(49+4.9(0))(10-(0)) \\ h=49\cdot10 \\ h=490 \end{gathered}$