Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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