As he lifts the sack to his chest from the floor
1) The buoyant force acting on an object immersed in a fluid is:

where

is the density of the fluid,

is the volume of displaced fluid, and

is the gravitational acceleration.
2) We must calculate the volume of displaced fluid. Since the titanium object is completely immersed in the fluid (air), this volume corresponds to the volume of 1 Kg of titanium, whose density is

. Using the relationship between density, volume and mass, we find

3) Now we can recall the formula written at step 1) and calculate the buoyant force. The air density is

, so we have

4) The weight of 1 Kg of titanium is instead:

So, the buoyant force is negligible compared to the weight.
E. Galaxy Cluster
Explanation:
A galaxy cluster, or cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by mutual gravity.
A megaparsec is a million parsecs and there are about 3.3 light years in a mega-parsec. Parsec is rather a natural distance unit for astronomers. The standard abbreviation of a mega-parsec is Mpc.
A parsec is approximately 3.09 x 1016 meters, a megaparsec is about 3.09 x 1022 meters.
Hence, 8 megaparsecs is gigantic size and that can be only of a galaxy cluster consisting of hundreds and thousands of galaxies bounded together.
Keywords: galaxies, parsec, megaparsec, galaxy cluster
Learn more about galaxy clusters and astronomical units from:
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The height of the roof is <u>3.57m</u>
Let the drops fall at a rate of 1 drop per t seconds. The first drop takes 5t seconds to reach the ground. The second drop takes 4t seconds to reach the bottom of the 1.00 m window, while the 3rd drop takes 3t s to reach the top of the window.
Calculate the distances traveled by the second and the third drops s₂ and s₃, which start from rest from the roof of the building.

The length of the window s is given by,

The first drop is at the bottom and it takes 5t seconds to reach down.
The height of the roof h is the distance traveled by the first drop and is given by,

the height of the roof is 3.57 m