Question

If a stone is tossed from the top of a 290 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 290, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.

Answer 1

The stone hits the ground when h(t) = 0 So the question is when does
-9.8t^2 - 10t + 290 = 0?
10 +- sqrt((-10)^2 - 4(-9.8)(290)) ALL OVER 2(-9.8) quadratic formula.

10 +- sqrt (100 - (-11368)) ALL OVER -19.6

10 +- sqrt ( 100 + 11368) ALL OVER -19.6
10 +- sqrt (11468) ALL OVER -19.6

Answers are
10 + 107.09 ALL OVER -19.6 which is 117.09/-19.6 = -4.95
and
10 - 107.09 ALL OVER -19.6 which is -97.09/-19.6 = 4.95

You have to throw out the negative answer since it represents time.

So after 4.95 seconds it would hit the ground

Answer 2

Thanks!!!!