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Galileo dropped balls of various weights from the top of the Leaning
Tower of Pisa to refute an Aristotelian belief that heavier objects fall
faster than lighter objects.
If the balls were dropped from a height of
54 meters, how long did it take for the balls to hit the ground?
Click here to know the answer!
What was the problem?
To solve the problem, we need to remember what we have learned in our early days of school. The gravity of the earth accelerates the falling object at the rate of 9.8 meter per second square. We know, the kinematic equation,
s = ut + (1/2) a t^2 .......(1)
where,
s = distance covered,
u = initial velocity,
a = acceleration,
t = time taken to travel distance s.
In this case, initial velocity must be 0 as it is dropped from height 54m. Again height here is the distance covered by the object. And the acceleration in this case is nothing but the acceleration due to gravity which is 9.8 m/s^2.
So putting s = 54 m, u = 0 m/s, a = 9.8 m/s^2 in equation (1) above,
54 = 0 x t + (1/2) x 9.8 x t^2
54 = 4.9 t^2
t^2 = 11.021
t = 3.3 seconds.
So theoretically both balls should take 3.3 seconds to reach the ground. But resistance due to air will make the difference in time taken by balls to hit the ground.
You are sitting with one opponent at an empty, round table. Taking
turns, you should place one dollar on the table, in such a way that it
touches none of the coins that are already on the table. The first
player that is not able to place a dollar on the table has lost. By
tossing a coin, it has been decided that you may start.
Which strategy will you follow to make sure you are guaranteed to win?
Trick to win this game always!
What was the game?
There is little trick with which you will always end on winning side in this Round Table Coin Game. Since you have got first chance to place the coin you should place the coin right at the center of the round table. Now for every next coin placed by opponent you need to place coin in such a way that it 'mirrors' opponent's coin.
Imagine line from the center to opponent's coin. Place your coin exactly opposite to that coin at distance equal to distance between center & opponent's coin. Or imagine a circle (with the center fixed at the round table) with opponent's coin lying on it's border. And place your coin at diagonally opposite point of point where opponent placed coin on that imaginary circle. (
Assume imaginary circle though it's not appearing perfectly in the image above)
In this way for every move of your opponent, you will have 'answer'
in form of space for placing the coin. This will continue until last
place left on the table with your turn of placing the coin in the end.
This is how to make sure you always on winning side in this 'Round Table Coin Game'!
