Here's what could be happening:
* Worn or broken transmission mounts: This is the most likely cause. They've become degraded over time, losing their ability to properly dampen vibrations and support the weight of the transmission.
* Worn engine mounts: While less likely to directly cause the engine to rise only in reverse, severely worn engine mounts can contribute to overall instability, making the transmission mount issue more pronounced.
* Transmission problems: Though less likely to be the primary cause of the *rising* engine, a problem within the transmission itself (e.g., internal damage, binding) might put extra stress on the mounts, exacerbating the existing issue.
What you should do:
1. Have a mechanic inspect the vehicle: This is crucial. They can diagnose the specific problem and determine the extent of the damage to the mounts or other components.
2. Don't drive the vehicle extensively: Continuing to drive with failing mounts could cause further damage to the transmission, engine, and other parts. The engine's movement is a clear indication of a serious issue.
3. Look under the car (carefully!): If you're comfortable and it's safe to do so, visually inspect the transmission and engine mounts for obvious signs of damage or wear (cracks, tears, significant looseness). However, a professional diagnosis is still needed.
Ignoring this problem could lead to more significant and expensive repairs down the line. Get it checked out by a qualified mechanic as soon as possible.