An explosion at ground level leaves a crater with a diameter that is proportional to the energy of the explosion raised to the 1/3 power; an explosion of 1 megaton of tnt leaves a crater with a 1 km diameter. an ancient impact crater is found with a 36 km diameter. what was the kinetic energy associated with that impact, in terms of (a) megatons of tnt (1 megaton yields 4.2 × 1015 j) and (b) hiroshima bomb equivalents (13 kilotons of tnt each)?

a)125 GT

b)9615384.6 Hiroshima bombs

Explanation:

We know that

D=k(E)^(1/3) (and I will keep D in km and E in MT of TNT)

D= diameter

Where k is a constant of proportionality.

We also have

1=k*(1)^(1/3), k=1

(a) For D=50, E=(D^3), so E= 125000 MT or 125 GT

(b) For Hiroshima equivalents, that's 125000 MT / 13 KT = 125000 MT / 0.013 MT = 9615384.6 Hiroshima bombs.

a) 3.024*10^12 MT

b) 2.326*10^14 units

Explanation:

Given:

- The relationship between diameter d of the crater and energy E is:

                                             d = k*E^(1/3)

- Where k is constant of proportionality

- Explosion of 1 MT of TNT creates 1 km diameter.

Find:

An ancient impact crater is found with a 36 km diameter

(a) megatons of TNT (1 megaton yields 4.2 × 1015 J)

(b) Hiroshima bomb equivalents (13 kilotons of TNT each)?

Solution:

- To evaluate constant k:

                                        1,000 = k*(4.2*10^15)^(1/3)

                                        k = 1.543*10^-5

- The relationship can now be expressed as:

                                       d = 1.543*10^-5*E^(1/3)

- For a crater of d = 36 km, the associated energy is:

                                      E = (36,000 / 1.543*10^-5)^3

                                      E = 1.2699*10^28 J

a)

                    1 MT of TNT   > 4.2 × 10^15 J

                                x         > 1.2699*10^28 J

                        x = 1.2699*10^28 /4.2 × 10^15  = 3.024*10^12 MT

b)     The E = 3.024*10^12 MT.

       1 unit of Hiroshima bomb is  = 0.013 MT of TNT

        Units of bomb = 3.024*10^12 MT / 0.013 MT = 2.326*10^14 units

b.

explanation:

10.0

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.