On a snowy day, max (mass = 15 kg) pulls his little sister maya in a sled (combined mass = 20 kg) through the slippery snow. when max pulls on the sled with 12 n of force, directed at an angle of 15° above the ground, how much work does max do on the sled as he pulls his sister 25 m in the snow?

290 J

Explanation:

1) Data:

i) Max's mass = 15 kg

ii) Maya in a sled's mass = 20 kg

iii) slippery snow ⇒ no friction

iv) F = 12 N

v) α = 15°

vi) d = 25 m

2) Physical principles and formula

i) The mechanical workg, W, developed by a constant force, F, that has an angle α with the displacement d, is given by the formula:

W = F × d × cos(α).

ii) The mass of Max is not relevant for the problem, nor the mass of the sled, since the fact that there is not friction, results in that the only force acting is F (12 N, α = 12°).

3) Solution:

W = 12 N × 25m × cos (15°) ≈ 290 J

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.