Problema Solution
If a stone is tossed from the top of a 330 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 330, 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 provided by our tutors
Put h (t) = 0
- 9.8 t ^2 - 10 t + 330 = 0
Here a = -9.8, b = -10, c = 330
apply quadratic formula
t = (-(-10) ±√((-10)^2 - 4*(-9.8)*330))/(2*(-9.8))
t = (10 ±√((-10)^2 - 4*(-9.8)*330))/-19.6)
t = (10 - √((-10)^2 - 4*(-9.8)*330))/-19.6), (10 + √((-10)^2 - 4*(-9.8)*330))/-19.6)
t = 5.32, -6.34
Ignore the negative value
so after 5.32 seconds stone will hit the ground.
Answer: 5.32 seconds