A large crate sits on the floor of a warehouse. Paul and Bob apply constant horizontal forces to the crate. The force applied by Paul has magnitude 48.0 N and direction 61.0∘ south of west. How much work does Paul’s force do during a displacement of the crate that is 12.0 m in the direction 22.0∘ east of north?

-570.4 J

Explanation:

Parameters given:

Force = 48N, 61° SW

Displacement = 12m, 22.0 NE

Work done is given by:

W = F*d*cosθ

To find θ:

θ = 61 + 90 + 22 = 172°

=> W = 48 * 12 * cos172

W = - 570.4 J

Hence, the work to be done is - 570.4J.

This value is negative because the applied force is opposite the direction of the displacement.

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.

answer; how far out of place which the object finished relative to the starting location;