need help on calculus problem A small rocket is launched vertically upward from
ID: 2892205 • Letter: N
Question
need help on calculus problem
A small rocket is launched vertically upward from the edge of a cliff 128 ft off the ground at a speed of 96 ft/s. Its height above the ground is given by the function h(t) = -16t^2 + 96t + 128, where t represents time measured in seconds. a. Assuming the rocket is launched at t = 0, what is an appropriate domain for h? b. Graph h and determine the time at which the rocket reaches its highest point. What is the height at that time? a. D = b. Which is the correct graph of h?Explanation / Answer
Answer is (C)
because h(t)=-16t^2+96t+128=0
that is -16t^2+96t+128+128=-128+128=0
which implies -16t^2+96t+256=0
that is t^2-6t-16=0
so (t-8)(t+2)=0
so t=8
since we know that rocket lands at 8 seconds and launches at o seconds so the midway through the flight is 8+0/2=4
that means rocket will hit maximum height after 4 seconds
maximum height is got by substituting t=4 in h(t) we get maximum height is 256
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