SOLUTION: I am truly stuck here with this homework problem. Can someone please help me?
If a stone is tossed from the top of a 310 meter building, the height of the stone as a function o
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Question 386723: I am truly stuck here with this homework problem. Can someone please help me?
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) = -9.8t2 – 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.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have a couple of basic problems with the function as you presented it. In the first place, your lead coefficient is wrong. 9.8 m/sec^2 is the acceleration due to gravity but the general height function for vertical motion near the surface of planet Earth is:
\ =\ \frac{1}{2}gt^2\ +\ v_ot\ +\ h_o)
Where 
and is the acceleration due to gravity (minus because gravity accelerates objects downward), 
is the initial vertical velocity component, and 
is the initial height.
Your function also presupposes a 10 m/sec downward (hence the minus sign) vertical component to the initial velocity component.
So your function is actually:
\ =\ -4.9t^2\ -\ 10t\ +\ 310)
You want to know the time it will take for the stone to hit the ground. Not surprisingly (I hope) the ground is 0 feet. So we make \ =\ 0)
and solve for t.
Looks an awful lot like a quadratic equation to me. Use the quadratic formula. We know that we will have a pair of real number roots. Any time your quadratic has opposite signs on the lead and constant coefficients, you always have real number roots. One of the roots will be a negative number which you should discard since you can't go back in time. The positive root is the number of seconds it will take for the stone to hit the ground.
Here's the quadratic formula in case you have forgotten:
John
My calculator said it, I believe it, that settles it
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