Final answer:
The pomegranate hits the ground at t = 0 seconds and t = 11 seconds. The pomegranate reaches its highest point at t = 5.5 seconds.
Step-by-step explanation:
To find the time the pomegranate hits the ground, we need to find the value of t when the height function f(t) equals 0. Setting -16t² + 176t = 0, we can factor out -16t to get: t(-16t + 176) = 0. This equation is true when either t = 0 or -16t + 176 = 0. Solving -16t + 176 = 0, we find t = 11. The pomegranate hits the ground at t = 0 seconds and t = 11 seconds.
To find the time the pomegranate reaches its highest point, we can find the vertex of the parabolic function f(t) = -16t² + 176t.
The formula for the x-coordinate of the vertex is given by t = -b/(2a), where a = -16 and b = 176. Plugging in these values, we find t = -176/(2*(-16)) = 5.5. Therefore, the pomegranate reaches its highest point at t = 5.5 seconds.