Atrain is moving at a constant speed on a surface and inclined at 10 degrees with the horizontal travels a distance of 400 m in 5 seconds. calculate the vertical velocity component of the train during the time period.

13.9 m/s

Explanation:

The velocity of the train along the inclined surface is given by the ratio between the distance travelled, d, and the time taken, t:

where we have

d = 400 m

t = 5 s

Substituting,

This is the velocity of the train along the inclined plane. Now we can find the vertical component of the velocity by using the formula:

where is the angle of the slope. Substituting, we find

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.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y