Nothing can escape the event horizon of a black hole, not even light. you can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 * 108 m/s, making all escape impossible. what is the radius of the event horizon for a black hole with a mass 5.0 times the mass of the sun? this distance is called the schwarzschild radius.

14740.7 m

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

M = Mass of black hole =

c = Speed of light =

Schwarzschild radius is given by

The radius of the event horizon of the black hole is 14740.7 m

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

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.