Question

If an object is dropped from a height of 141 feet, the function h(t) = -16t^2 + 141 gives the height of the object after t seconds. When will the object hit the ground?

Answer 1

The height of the object is given by:

`h(t)=-16t^2+141`

to know when will it hit the ground we equate the expression to zero and solve for t:

`\begin{gathered} -16t^2+141=0 \\ 16t^2=141 \\ t^2=(141)/(16) \\ t=\pm\sqrt[]{(141)/(16)} \\ t=\pm\frac{\sqrt[]{141}}{4} \end{gathered}`

Since time has to be positive it takes:

`\frac{\sqrt[]{141}}{4}\text{ seconds}`

for the object to hit the ground. This is approximately 2.97 seconds.