if a stone is tossed from the top of a 310 meter building, the height of the stone as a function of time is given by h(t)=-9.8t^2-10t+310. 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.
To find the time it takes for the stone to hit the ground, we need to determine when the height, h(t), becomes equal to zero. We can set the equation h(t) = 0 and solve for t. In this case, the equation is:
0 = -9.8t^2 - 10t + 310
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = -9.8, b = -10, and c = 310. Let's substitute these values into the formula:
t = (-(-10) ± √((-10)^2 - 4(-9.8)(310))) / (2*(-9.8))
Simplifying:
t = (10 ± √(100 + 12160)) / (-19.6)
t = (10 ± √12260) / (-19.6)
Now, we can calculate the two possible values for t:
t1 = (10 + √12260) / (-19.6)
t1 ≈ -9.53 seconds
t2 = (10 - √12260) / (-19.6)
t2 ≈ 6.23 seconds
Since time cannot be negative in this context, we disregard t1 as an extraneous solution. Therefore, the stone will hit the ground after approximately 6.23 seconds.