# Velocity of blocks under different situations

Height of all blocks is 100m.

CASE 1:
Blocks are at a distance of 100m in height. When they reach the ground , velocity of 1st block must be higher than velocity of second block due to the extra distance of 100m which would result in increased velocity.

The most important scenario to consider here is 2nd & 3rd.1st is used for remembering all the possible scenarios.

CASE 2: When both the blocks are tied to each other with a string which is unbreakable. After touching the ground , since the upper block is at a higher distance of 1m than 2nd block. Will their speed remain same ? If yes , How ? Also , what I think is significant to notice in this case is that maybe the 2nd block is also putting pulling force on 1st block since they are tied.

CASE: 3 In this case , both blocks were just kept together at the time of falling. Will the speed of both blocks remain same ? Can the blocks separate from each other ? I think velocities of block will not be same.

• What fluid are you operating in, and what are the masses of the blocks? Have you considered the terminal velocity of the objects (referring to your usage of "must" in Case 1)? May 25, 2022 at 12:52
• @JonArnt 1kg mass of block. May 25, 2022 at 13:26
• "Height of all blocks is 100m." How about edit your question so we can understand what you are trying to do. What you should do is go look at the equations of motion. Velocity is a function of time in freefall, not initial height. May 25, 2022 at 17:48

Without considering drag, we can assume $$E = mgh = mv^2/2$$, and $$v = \sqrt{2gh}$$.

Case 1 - The higher block went through a longer distance, thus it has the higher terminal velocity.

Case 2 - The blocks are essentially acting as a unit block, thus, the terminal velocity is the same, and the travel distance is measured to the mass center of the combined blocks.

Case 3 - The terminal velocities are the same for both blocks, as both went through the same distance - the travel distance is measured from the mass center of each block to the ground.

Ignoring terminal velocity and air resistance, if you tie one block with another, then the force of gravity will work through the center of mass,and that will define the final speed. Ground facing particles of the block will try to move faster, as they are closer to the attracting mass, and the others not so much but the tension forces among particles will sort it out. The tension force will accelerate some particles and decelerate others, forcing the same velocity everywhere.

Then, if however, both tied blocks were released under gravity, then they actually travel the same distance and time until the lower block strikes ground. Think of it : if the upper block starts x meter higher, it always remain x meter higher until the lower block hits the ground.

If they are not tied to each other, only say "glued together", then the lower block will experience a higher force of gravity than the higher one. This is called tidal force. This can be sufficient to break the glue and seperate the blocks. This is why comets break apart when they come too close to , say, Jupiter or other large bodies