That is a contrail from an airplane, not a rocket.
The wideness of the trail at the bottom part of the photo makes it clear that it has been lingering for some amount of time. The distortion is clearly due to the effect of wind shear acting on the lingering trail, not due to radical maneuvers.
Rocket engines burn for a relatively short time, and rockets have steeply climbing trajectories. If that dot at the end were an actual rocket, the portion of the trail at the bottom of the photo would be only a few minutes old at most, which is unlikely to be enough time for changes in wind velocity with altitude to produce that much distortion in the lingering contrail. Also, it is difficult to think of a scenario where a rocket's steeply climbing exhaust trail would be sunlit on the bottom and shaded on the top. The opposite would normally be true-- as in this incredible photo from the Space Shuttle mission STS-98.
Image from NASA
It is not that uncommon for an airplane's basically horizontal contrail to look like this. The distant portion, which is at the bottom of the photo, may be well over five minutes old, allowing wind shears more time to distort the trail-- although in truth this much distortion would be more common in a case where the trail had been lingering for several tens of minutes, with the airplane itself long gone. But in fact I have taken a photo much like this, with the airplane still approaching, and joked with somebody standing beside me about the "crazy maneuvers" that it looked like the aircraft had undergone. Of course when the aircraft passed overhead it was clearly just a commercial airliner flying in a straight line.
The sun is clearly located toward the lower right of the picture--see the diagonal shadow streaking up and left from one of the sharp "bights" in the trail. Note that a similar diagonal shadow line is faintly visible running up and left from the very bottom right corner of the photo. Follow both lines down and right and see that they converge at a point below and right of the lower right edge of the photo-- the sun is clearly below the horizon as seen by the camera. The sun is also clearly below the horizon as seen from the aircraft's current position-- as suggested by another answer, the aircraft has clearly flown past the terminator of the sunrise or sunset, passing into the shadow of the earth itself. This would be very unlikely with the near-vertical trajectory of a rocket. In the rare event that it did happen, the photo would look quite different than this-- you would see the trail rising up steeply and then arcing over toward a more horizontal trajectory in a way that just doesn't fit what we see in this photo.
While other answers have pinned down with confidence the exact time and location of the flight, note that the principles applied in this answer could be applied to any similar photo without knowing any more information.
Let's close out this answer with a few more notes on the spectacular photo from the launch of STS-98. This mission was launched just after sunset. Although the trajectory is arcing over the toward the east, the extreme altitude gained in the vertical part of the trajectory has caused the vehicle to pass from shadow into sunlight, rather than vice versa. Note the long shadow, cast through the still-sunlit upper atmosphere by part of the exhaust plume itself, ending at the anti-solar point just below the moon, which is about half a day from being exactly full. The shadow is made more visible by the fact that that much of the dust-and-moisture-filled lower atmosphere between the observer and the shadow is already shaded by the earth itself, reducing glare.
Someone standing 5 miles away would have seen something quite different-- the shadow line might not have been visible at all, or a different part of the trail might have been aligned to cast a visible shadow line. Of course, the shadow (if visible) would still slant through the sky at the same angle, and would still end at the distant anti-solar point, just below the almost-full moon.
For a contrail or exhaust plume to cast a visible shadow through the atmosphere like this, a significant segment of the shadow must be directly aligned with the observer or camera. This can only happen when a significant segment of the contrail itself is directly aligned with the sun as seen by the observer or camera. In other words an imaginary line extended from that linear segment of the contrail must appear to pass directly through the sun as seen by the observer or camera. The easiest way to catch a glimpse of this phenomena in action is watch for an instance where a long, linear contrail is just upwind of the sun as seen from your position. As the contrail drifts through the sun and then downwind of the sun, its aerial shadow will appear and then vanish again. Then another observer standing further downwind will have a chance to observe the same thing. The aerial shadow from a contrail or exhaust plume is like a pane of window glass-- it is invisible unless you are looking at a significant length of it directly edge-on.
