Final answer:
The soccer ball takes 6 seconds to reach the top of its trajectory in symmetrical motion, considering it takes a total of 12 seconds to ascend and descend.
Step-by-step explanation:
The question asks how long it takes for a soccer ball to reach the top of its trajectory if the total time for the ball to go up and come back down is 12 seconds. The motion of the ball can be considered symmetrical concerning time because the time it takes to go up is the same as the time it takes to come down, assuming no air resistance. Therefore, if the total time is 12 seconds, then it takes half of that time for the ball to reach the top of its trajectory.
So the answer is: a) 6s. Because gravity acts symmetrically on the ball during its ascent and descent, the time to reach the peak is equal to half the total time of flight. When the ball is kicked into the air and comes back down without any interruptions or changes in forces (aside from gravity), it spends half of the total time going up to the highest point and the other half coming back down.