A battleship fires a heavy caliber gun towards a fighter aircraft that flies at an unknown altitude. The maximum speed of a bullet is 520 m/s and height to the exit of the riffle is 9 m. The gun is kept at angle of elevation of 30o .( Ignore air resistance.) (a) Write the position vector r(t)

The position vector

Explanation:

Given that:

The maximum speed of the projection of the bullet = 520 m/s

The height to the exit of the rifle = 9 m

The angle of the elevation = 30°

Taking the vector position with respect to the horizontal axis and vertical axis; we have:

Initial Velocity:

At the horizontal axis

At the vertical axis

The displacement in the (x) direction can be computed as:

where;   ; a = 0 ; t = t

The displacement in the (y) direction can be computed as:

where;   a = -g

∴

The position vector r(t) =

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.