This comes back to a combination of visualizing a parabolic pathway and knowing the shortcut equation where vt = 10t for free from rest. The second half of a parabolic flight in the y-direction follows the same kinematics equations as free fall from rest. The second half of a parabolic flight is mirror image of the first half, but in the opposite direction.
With these concepts in mind, let's look at the givens. They tell us that initial = 45 m/s straight up, so vapex = 0 and vfinal =45 m/s straight down. The fall time is about 4.5 seconds if we use vt = 10t, so the total flight time is about 9 seconds. This means by symmetry, the ball will have the same speed and height at 1-sec as it does at 8-sec, the same speed and height at 2-sec as it does at 7-sec, the same speed and height at 3-sec as it does at 6-sec, and so on.
The first answer choice tell us it is traveling upward at the 3.0-sec mark, which makes sense since it's in its first half (upward half) of flight. The second answer choice tells us it is at the same height at the 2.0-sec mark and the 7.2-sec mark, which seems wrong but really close to what we visualized. The third answer choice tells us it is at the same height at the 3.2-sec mark and the 6.0-sec mark, which again seems wrong but really close to what we visualized. Both answers can't be wrong, so we need to consider whether they complement one another. Both add to 9.2 sec, which would mean that they both have an apex time of 4.6 seconds, very close to 4.5 seconds. Given that g = 9.8 and not 10, the actual apex time is slightly higher than 4.5 seconds, so 4.6 seconds seems viable. So now that we've been a little more anal in our view, we can say that the total flight time is actually 9.2 seconds and that the ball will have the same speed and height at 1-sec as it does at 8.2-sec, the same speed and height at 2-sec as it does at 7.2-sec, the same speed and height at 3-sec as it does at 6.2-sec, and important to this question the same speed and height at 3.2-sec as it does at 6.0-sec. We find that choices B and C complement one another.
Lastly, we knew that the apex happened around 4.5 seconds, and now know that it's actually 4.6 seconds, but even with the slight error we can determine that there is no way for the apex to occur at 6.6 seconds.
So you did great getting choice D as the best answer quickly. This is where you need to make a choice. Can you move on and feel a little uncertainty without it linger or do you need to fully solve this question and eliminate the other three choices before you can move on. If the uncertainty is going to haunt you and take away from your focus on future questions, then spend the time to resolve it in your mind. However, as you practice more and more, try to learn to squelch the need to double check everything. You are looking for a best answer as fast as you can get it, without overthinking or making careless errors. It takes a while to be able to do this.
