Final answer:
The rocket takes 7.5 seconds to reach its highest point and the height of the rocket at its highest point is 900 feet.
Step-by-step explanation:
The equation for the height of the rocket is given by h = 240t - 16t², where h is the height in feet and t is the time in seconds. To find the time it takes for the rocket to reach its highest point, we need to find the vertex of the parabolic equation. The vertex is given by the formula t = -b/2a, where a = -16 and b = 240. Substituting the values in, we get t = -240/(2*(-16)) = 7.5 seconds. Thus, it takes 7.5 seconds for the rocket to reach its highest point.
To find the height of the rocket at its highest point, we substitute the value of t into the equation h = 240t - 16t². Substituting t = 7.5, we get h = 240(7.5) - 16(7.5)² = 1800 - 900 = 900 feet. Therefore, the height of the rocket at its highest point is 900 feet.