The earth has a mass of 5.98 × 10^24 kg and the moon has a mass of 7.35 × 10^22 kg. The distance from the centre of the moon to the centre of the earth is 3.84 × 10^8 m. A rocket with a total mass of 1200 kg is 3.0 × 10^8 m from the centre of the earth and directly in between the earth and the moon. Find the net gravitational force on the rocket from the earth and moon.

F = 4.48N

Explanation:

In order to calculate the net gravitational force on the rocket, you take into account the formula for the gravitational force between two objects, which is given by:

        (1)

G: Cavendish's constant = 6.674*10^-11 m^3kg^-1s^-2

r: distance between the objects

You have a rocket at the middle of the distance between Earth and Moon, then, you have opposite forces on the rocket.

If you assume the origin of a system of coordinates at the rocket position, with the Moon to the left and the Earth to the right, you have:

      (2)

Me: mass of the Earth = 5.98*10^24 kg

Mm: mass of the Moon = 7.35*10^22 kg

m: mass of the rocket = 1200kg

r1: distance from the rocket to the Earth = 3.0*10^8m

r: distance between rocket and Moon = 3.84*10^8m - 3.0*10^8m = 8.4*10^7m

You replace the values of the parameters in the equation (2):

The net force exerted over the rocket is 4.48N

they should be similar or the same

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.