Consider the problem were we decided that Indy probably wouldn’t survive due to the radiation exposure. But let’s look at the problem from a projectile motion stand point.

So, how to start? Indy and his fridge are in the air for 10 seconds. That means he spends 5 seconds going up, and 5 seconds going down. The acceleration due to gravity is about 10 meters per second per second toward the center of the Earth (we know it is really 9.81 but lets simplify things), so on the way up, he is slowing by 10 meters per second each of those 5 seconds. At the top, his vertical velocity is 0 for an instant before he begins to fall. So if he slows by 10 m/s every second for 5 seconds, his initial vertical velocity must have been 50 m/s. Now what? Well, we have to use some trigonometry. Now that we know his vertical velocity was 50 m/s, if we estimate his launch angle to be about 5 degrees, we can use the following relationship to determine how fast the fridge was launched:

sin ѳ = V_{vertical} / V_{launch}

Once you have the correct launch/initial velocity please relate this number to something known in order to determine if this is a survivable trip for a human.