On a sky coaster (human pendulum) that reaches 20 meters from it's equilibrium position, a man of 70 kg is able to reach a maximum speed of

19.8 m/s

Explanation:

During the motion of a pemdulum bob, it casually converts kinetic energy to potential energy and vice versa.

A pendulum bob reaches its maximum speed at a position closest to its equilibrium position and has its lowest when it is farthest from the equilibrium position.

The maximum speed of a pendulum bob based on the mass involved and the maximum displacement from the equilibrium position is obtained from

Maximum kinetic energy = Maximum potential energy

Maximum potential energy occurs at the farthest point from equilibrium, that is,

P.E(max) = mgh

Maximum kinetic energy = ½mv²

½mv² = mgh

v = √2gh

g = acceleration due to gravity = 9.8 m/s²

h = farthest height from equilibrium position = 20 m

v = √(2×9.8×20) = 19.8 m/s

Hope this Helps!!!

their crystal patterns have been disrupted by stress

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.