Acannon ball at ground level is aimed 30 above the horizontal and is fired with an initial speed of 125 m/s. how far away from the cannon will the cannonball hit the ground?

691 m

Explanation:

In these problems the time a ball is in the air is determined by the gravitational acceleration (y-coordinate) and the distance it travels is related to the velocity in the x-coordinate.

First get the x and y components of the initial speed.

Initial speed has a magnitude of 125 and a direction of 30°

speed in x = 125 cos 30° = 108.3 m/s

speed in y = 125 sin 30° = 62.5 m/s

The time it takes to the ball to reach the highest height (when the speed in the y-coordinate is 0) is:

0 = 62.5 - 9.8*t

t = 6.38 s

With the time you can calculate the distance travelled in the x-coordinate at a constant speed of 108.3.

d = vt

d = 108.3 * 6.38

d = 691 m

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.

3. dark matter

empty space could also be a simple vacuum