An invading barbarian whirls a stone in a leather sling. If the sling is 90 cm long, and the velocity of the stone is 90 m/s, what is the centripetal
acceleration of the stone?

Explanation:

Centripetal acceleration is expressed as shown:

a = v²/r

v is the velocity

r is the radius

If the length of the sling is 90cm, hence the circumference of the circular path is 90cm

Since C = 2πr

0.9 = 2πr

r = 0.9/2π

r = 0.9/2(3.14)

r = 0.9/6.28

r = 0.143m

Get the centripetal acceleration:

a = 90²/0.143

a = 56,643.36m/s²

Hence the the centripetal  acceleration of the stone is  56,643.36m/s²

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.