What would the collision between a (large) solid planet and a gas giant be like? Assuming a Jupiter-like planet and an Earth-like planet (Except, say... half the mass of Jupiter), what would happen when the two collide? 
For clarification: What would the actual collision be like?
Here on earth solids always just travel through gases "easily" (with some friction). Would the solid planet similarly just pass into the gas planet?
I assume there is some type of solid (or molten) core in Jupiter. Would the "real" collision be between the solid planet and the gas planet's core?
If the gas planet had no molten or solid core (all gas) would there be minimal changes to the solid planet?
Would the answer to this question change if both planets had Earth-like masses?

Edit 
This answer makes me imagine it would be like two liquid spheres colliding, would that be a correct view?
 A: I'm seeing a lot of references to Roche limits and the like in the answers here, but to me, that is implying a far slower process than what I would think would be described as a "collision". Just assuming a collision velocity no greater than that starting the two planets at rest and letting them fall together under their own mutual gravity, they're going to be going so quickly by the time they collide that there certainly won't be time for them to break apart due to being within the Roche limit.
If we take this question as Earth colliding with Jupiter, then technically, theoretically, yes, Earth would begin to break apart, but we're talking about a minimum collision speed here of about 60 km/s (Jupiter's escape velocity). The entire collision at that speed, from first contact of atmospheres to centers-of-mass coinciding, is only about 20 minutes. So while technically one or both would begin to break apart, the differential acceleration between their nearest and furthest points will be on order of about 4 m/s², making the total breakup on order of about 4800 km, or around a third of the diameter of the Earth. Not insignificant, but fairly trivial in terms of the overall impact's effects. (Consider the difference between a cannonball splashing into a barrel of water vs. a dumbbell. Yeah, technically they'll behave somewhat differently, but in terms of the level of catastrophe, it's pretty trivial.)
Far more important is to consider that at the magnitudes of forces and velocities involved in a collision like this, everything behaves as a fluid. So yes, the analogy of it being closer to imagining two spheres of water colliding than two solid objects is quite apt.
Interestingly, there's a theory that almost exactly this happened in Saturn's past: a roughly Earth-sized object may have collided with it in the distant past. This did not, of course, result in Saturn breaking up, but it may have resulted in 'splashing' its core into something quite a bit less orderly and more 'fuzzy' than suspected before. It may even still be 'sloshing' in a sense, creating some of the resonances responsible for the specific patterns of its rings!
I'm also seeing a lot of assumptions of velocities quite a bit lower than Jupiter's escape velocity, but... how would this happen? If we put ourselves in a Jupiter-centric frame of reference (but non-rotating), then the least-fast object that could conceivably collide with it would be one that is stationary at infinity, i.e. at its escape velocity. In order for a colliding object to be going slower than that, it would need to pop into existence at some finite distance from it, which can't really happen outside a simulation.
So, combine the minimum speed possible for this scenario (60+ km/s²), the short duration of the collision (1200 seconds or so), and the sheer forces and amount of heat involved, and what you'd have is more of a 'splash' of a smaller sort of egg-shaped ellipsoid of water hitting a much larger and more massive sphere of water.
For an intuitive sense of what it might look like, check out some simulations of the collision that is theorized to have created the Moon, such as: https://youtu.be/o2lRpiediP8?t=340 This would be quite a bit less dramatic, with 300:1 mass difference instead of 10:1, but still enough to hopefully give some idea.
A: Currently there's no defined upper limit on how massive a terrestrial planet can be, but 0.5 Jupiter masses might be too high. A planet this massive will be able to retain volatiles left from the primordial cloud and would become a gas or an ice giant.
But let's assume that for some strange reason we do have a rocky planet half the mass of Jupiter. Shoemaker-Levi 9 comet that famously collided with Jupiter in 1994 has been pulled apart by tidal forces. But that was a comet with an estimated average density 500 $kg/m^3$. 
By comparison our super-sized Earth will have a radius of some 33000 km (assuming the density around 6500 $kg/m^3$) compared to current 6300 km. It will also have a surface gravity of approximately 60 $m/s^2$ or 6g. This all will allow it to withstand Jupiter's tidal forces much better. In fact, my quick calculations show that in the tidal force contest the rocky planet would win due to much higher density.
As it approaches to within 1 Jupiter radius from Jupiter's cloud tops, it would start stripping atmosphere from the gas giant. This won't last for very long though.
The rest really depends on multiple parameters like angle and velocity of the impact, but in general case from what I can see as soon as our rocky planet enters the lower atmosphere of Jupiter the tidal stress would become so great that both the rocky planet and the Jupiter will lose gravitational cohesion and break apart.
The ensuing collision really has to be simulated. But in general, large amounts of material will be thrown away, the remaining mass of both planets will eventually coalesce into a new planetary body. The size and mass of the new planet will largely depend on initial conditions. It's very likely that a large percentage of gases (hydrogen and helium) will be lost and the newly formed body will be either a gas giant (albeit with lower ratio of gases of the total mass) or will end up as a super-sized ice giant.
A: 
Assuming a Jupiter-like planet and an Earth-like planet (Except, say... half the mass of Jupiter), what would happen when the two collide? For clarification: What would the actual collision be like?

I think you are looking for a few things that aren't exactly clear.  First, this isn't like a small baseball slamming into a water balloon.  The impacting object's body must be strong enough to hold together when passing through the Roche limit.  Since Earth is basically a hard Ni-Fe core surrounded by molten rock encrusted by mostly silicate-based rock, it's more like an egg with a steel marble inside than a baseball.
Even at the typical high speeds of interplanetary collisions (i.e., >10-20 km/s starting speeds before gravitational acceleration), the impacting body will be ripped apart by the gravity of a Jovian-like planet (assuming the impactor is the smaller of the two by a lot, e.g., Earth vs. Jupiter).  So if we ignore glancing blows and make it a simple 1D problem of radial impact, the impactor will tear apart as it accelerates toward the planet sending a lot of smaller (relative to the original body) pieces into the atmosphere.

Here on earth solids always just travel through gases "easily" (with some friction). Would the solid planet similarly just pass into the gas planet?

Nope.  Solids only pass through "easily" when they move slowly.  As their speed increases relative to the fluid, their drag increases parabolically with speed.  At 10-20 km/s, the impactor will almost certainly be passing hypersonic speed for the atmosphere of the larger body, thus generating strong shock waves which decelerate, compress, and heat the gas.  These processes can heat the gas so much that it can melt most solids and even lead to ablation.
So no, it would not just pass into the gas giant, the numerous falling, solid bodies would become super-heated projectiles.

Would the answer to this question change if both planets had Earth-like masses?

Not necessarily.  The Roche limit depends upon density, not mass alone.  If an Earth planet came near a much denser planetary body of the same size, Earth would be the one torn apart by the gravitational forces.
If we ignore all of these factors and just imagine to planet-sized rocks colliding at >10 km/s, then the result would be a catastrophic spray of molten debris that may or may not reform into a new planetary body, depending on how the two objects collided.
A: This is an interesting question. Basically it's very similar like any meteorite collision. The gas planet makes here no other difference, but that there will be no crater. 

Assuming a Jupiter-like planet and an Earth-like planet (Except,
  say... half the mass of Jupiter), what would happen when the two
  collide? For clarification: What would the actual collision be like?

The mass is only a part of the story, the collision velocity has much greater influence as the Kinetic energy is $1/2mv^2$, and at collision this all will be transferred to pressure, and then agin to kinetic energy. If this new kinetic energy is above the escape velocity, then there will be a truly "explosion" which causes the planets to be broken and lost material in the space. If this velocity can't be reached, then the collision will be very similar like an elastic collision. 

Here on earth solids always just travel through gases "easily" (with some friction). Would the solid planet similarly just pass into the gas planet?

No, The friction based burning of meteorites, changes nothing in the fact that the entering in the atmosphere causes pressure waves. Even though these pressure waves travels oft behind the meteorite, similarily like the sound waves behind hypersonic airplane. But as long these pressure waves doesn't produce escape velocity, the collision will be very similar to elastic collision. 
Let's calculate something. But please note that the velocity is a really important factor here.
If 1/2 Jupiter would be collided by the mass of Earth?


*

*The collision would be perpendicular to the travel direction of 1/2 Jupiter 

*The velocity of the colliding "Earth" would be same as orbiting Earth; 30 km/s

*The escape velocity of "1/2 Jupiter" is 0.707 x Jupiter; 42 km/s


As the collision velocity is allready smaller than the escape velocity, there is no mechanism which could produce an "explosion" which would lead to a significant material loss; some amount of gases of the upper atmosphere of "1/2 Jupiter" will be blown away, but the collision is mostly absorbed. It's not even possible that the Earth shoots through the "1/2 Jupiter" as, the velocity is not enough for that even in entrance.
Note that the result of this collision would change if the the planets make a frontal collision; The orbital speed of Jupiter is 13 km/s, und thus such a collision would be able to produce escape velocities to "1/2 Jupiter", but not to Jupiter.  

Would the answer to this question change if both planets had Earth-like masses?

Yes, This really makes a difference. The escape velocity of Earth is only 11.2 km/s, so the collision would produce velocities able to escape the gravity. And it might be even possible that the Earth would shoot through this "gas mass earth". Let's calculate. 
If this Gas Earth would had similar density as Jupiter; 1/4, it's volume is 4 x time's bigger and radius is thus 1.6 x times bigger then that of normal Earth. This means that the Earth would collide only to a "fluid cylinder" with length of 3.2 and diameter of 2 Earth radius. Thus The Earth would collide only to a part of it's mass. The Result would be that the Solid earth would go through with reduced velocity and the gas planet would mostly explode, but some of it's mass would be catched by the solid earth.
A: First of all, we have to look at the scenarios. First. If an earth sized planet collides with a gas giant. It is quite simple. As the smaller planet crosses the roche limit of the gas giant, it is broken up into pieces which either crash into the gas giant, fall into orbit around the gas giant or are so fast that they escape ino space, in a brilliant show of celestial fireworks. Or, the planets could be colliding at great speed. Then the same thing will happen. Only difference is that most of the pieces of the destroyed planet will be flung into space as there is greater momentum in the system and hence velocity. If the gas giant and the rocky planet were around the same size, the results will be different. As they go closer, they begin to exchange mass. They may fall into binary orbit around each other. Or if they are fast enough, they may smash into one another. The force of their gravity and rotation, rips the two planets apart like a cosmic shreder. Lame, i know. Then the gravitational attraction between the ensuing cloud of gas, rocks and dirt pulls it all back together. In effect, the two planets merge. If we are to really describe what will happen here, it will be like this. Temperatures rise as particles are accelerated through gas molecules. Flaming pieces of rock are spewed in all directions. The two planets drill each other into pieces, and then the pieces conglomerate into a new molten plant, with a very robust atmosphere. Which would then begin to bleed out into space, as due to all the mass lost in the collision event, the gaseous atmosphere from the gas giant is too large for the new plant to hold. Once the atmosphere is stabilized, a new planet bigger then either of the two parent planets has been formed.
Just as a note, i dont think either of these planets will survive, as the jetstreams of matter may accelerate it right into the star in its solar system. Or away.
A: Let's first conclude that Jupiter average density is slightly bigger than water's $\approx 1.3 ~\text{g/cm^3}$. Thus collision effect will be comparable to water sphere collision with solid body. And of course that depends on impact speed too. There is pretty good paper which analyzes water droplets collision with solid surfaces, namely Waterdrop Collisions With Solid Surfaces,
Olive G . Engel, 1955. There you will find out that De Haller estimated impact pressure between solid surface and water column, which is :
$$ P_{impact} = \frac {v~\rho_1c_1}{1+({\rho_1c_1}/{\rho_2c_2})} $$
Where $v$ is relative speed of water column with respect to solid surface; $\rho_1, \rho_2$ densities of water and solid; $c_1,c_2$ - sound speeds in water and in solid material where droplets are landing.
Substituting Earth average density of $5.5 ~g∕cm^3$, sound speed in water and in concrete of $3.2 ~km/s$  (I've chosen concrete because it has comparable density to that of Earth) and impact speed $v=v_{_{Jupiter}}+v_{_{Earth}}$ which is $42 ~km/s$, i.e. the double averaged orbital speeds between Jupiter and Earth, accounting for hypothetical collision in a middle-distance orbit between Jupiter and Earth as if they were circling in the same orbit, but in opposite directions.
This gives approximate impact pressure of $\approx 60 ~\text{GPa}$, which is comparable to detonation pressure of pure CL-20, the most powerful high explosive in mass production ! So this level of detonation between Jupiter and Earth probably will blow-out bunch of Jupiter's metallic Hydrogen into outer-space in the same time producing shock-wave to Earth too, accounting to smaller degree of Earth surface abruption, so certainly Earth will not look the same after collision- imagine exploding millions of CL-20 explosive bombs across half surface area of Earth !
In addition to that Earth probably should slow-down, due to liquid metal hydrogen viscosity, upon reaching rock and icy Jupiter core. Besides, due to temperature increase, because of high collision energy and due to fact that Hydrogen is highly flammable,- there is big risk of Hydrogen being ignited. So overall,- Earth and Jupiter collision would make a nice Kaboom !
