Using the kinematic equation, the stone takes 4 seconds to reach its highest point after being thrown upwards from a 320-foot cliff at 128 ft/sec with an acceleration of 32 ft/sec² due to gravity.
The subject of this question is Physics, and it pertains to the behavior of a falling object under the influence of gravity, which is a topic typically covered in a high school curriculum. To answer part (a) of the question regarding how long a stone takes to reach its highest point when thrown upward from a cliff, we can use kinematic equations that describe motion under constant acceleration. The stone is thrown upward with an initial velocity of 128 ft/sec, and we are to find the time it takes for the stone to reach the peak of its trajectory, where its velocity will be 0 ft/sec. Since the acceleration due to gravity is 32 ft/sec² downward, we can use the following kinematic equation, which relates velocity, acceleration, and time:
v = u + at
Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. We set v to 0 since the stone will momentarily stop at the highest point, so the equation becomes:
0 = 128 ft/sec - (32 ft/sec²) × t
Rearranging the equation to solve for t gives:
t = (128 ft/sec) / (32 ft/sec²) = 4 sec
Therefore, the stone takes 4 seconds to reach its highest point.