Launching a rocket A small rocket is launched vertically upward from the edge of a cliff 80 ft off the ground at a speed of 96 ft/ s. Its height above the ground is given by the function ?h?(?t?) = ?16?t?2 + 96?t? + 80. 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?

Step-by-step solution Step 1 of 4 Step 2 of 4 a) Assume that the rocket is laun ched at t =0. The domain offunction h (t) represent the time from the beginning of rocket mouvement (t=0) until the rocket hits the ground. When the rocket hits the ground then its height is equal to zero. Therefore, if we want to find the domain o f function h(t) we must solve the equation h (t)=0. Let’s rearrange this equation.