Question

Question #b22b0

Answer 1

Assuming the acceleration caused by gravity is constant and approximately equals to `g~~9.81m/sec^2`, directed vertically down, the time until a pin returns back equals to

`T ~~ 1.67(sec)`

Explanation:

The pin will go up against the only force - the force of gravity - that causes its deceleration since it's directed against the initial velocity.
Then it will go down the same distance and the same time as it went up.

The fact that the time of descending equals to the time of ascending is obvious and follows from the fact that acceleration caused by the gravitation is constant. By the way, the final velocity of the pin, when it comes back, would be equal in value to an original velocity, but directed downward.

Any object on the surface of the Earth is a subject of the force of gravity that, if the object is not supported, will cause its acceleration `g~~9.81m/sec^2` directed vertically down.

Firstly, let's calculate the time of ascending of a pin thrown up with a velocity `V=8.20m/sec`. With negative (against the movement) acceleration of `g` the object will lose the speed by `g` meters per second every second, so the time it loses all its speed equals to
`t = V/g`

At this point we can determine the overall time until the pin returns back to a juggler by just doubling the time above:
`T=2t = 2V/g ~~ 2*8.20/9.81 ~~ 1.67 (sec)`