Answer :
Final answer:
The object will hit the ground in approximately 3.94 seconds and the velocity upon impact will be -126.08 feet per second.
Explanation:
If an object is dropped from a 157 foot high building, its position is given by the equation s(t) = -16t² + 157.
To find when it will hit the ground, we need to find the time when the position is equal to zero.
We can solve the equation -16t² + 157 = 0 using the quadratic formula.
The positive root is the one we are interested in, which is t = 3.94 seconds.
To find the velocity upon impact, we can differentiate the position function with respect to time.
The derivative of s(t) = -16t² + 157 is v(t) = -32t.
Plugging in the time
t = 3.94 seconds,
we get v(3.94) = -126.08 feet per second.
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