Question 77426
a)
To find the time at the highest point, lets complete the square for {{{H(t)=-16t^2+96t+4 }}} so we can convert it into vertex form:

*[invoke completing_the_square -16, 96, 4]

So the vertex is (3,148) where the first coordinate is t, so t=3. 


b)
Since the rocket explodes at the vertex (the highest point), the height of the explosion is 148 ft (ie it's the y coordinate of the vertex).