The ceiling of an arena is 79 m above the floor. What is the minimum speed that a thrown ball would need to just reach the
ceiling?
m/s

39.37 m/s²

Explanation:

We are given;

Height from the floor to the ceiling as 79 m

We need to determine the minimum speed for the ball to reach the ceiling.

We will need to know;

The potential energy of the ball at the ceiling will be maximum while the kinetic energy will be minimum.This means, that the kinetic energy that was possessed by the ball while in motion was converted to potential energy.

Therefore, potential energy = kinetic energy

That is ;

mgh = 0.5 mv²

simplifying it, we get;

gh = 0.5 v² , taking g as 9.81 m/s²

Then;

v² = 79 m × 9.81 m²/s × 2

v² = 1549.98

v = √1549.98

  =39.37 m/s

Therefore, the minimum speed the ball needs to reach the ceiling is 39.37 m/s²

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.