Question 1158945
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(a)  It will happen, when h(t) = 102,  i.e.


     -16t^2 + 91t + 15 = 102.


     It is your basic equation to start.

     Solve it by any way you want.


     You will get 2 (two) roots.


     One root is the solution when the object moves up;  the other root is the solution, when the object falls down.



(b)  It will reach the ground, when h(t) = 0, i.e.


     -16t^2 + 91t + 15 = 0.


     So, this time you should solve this equation.
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Happy solving (!)