A bicyclist is traveling 10 m/s at 30 degrees south of east. The cyclist and bicycle have a combined mass of 70 kg.
First, determine the momentum of the cyclist and bicycle using the
momentum equation directly. Then solve for momentum by separating
velocity into x- and y-components, using the momentum equation for
each component, and finding the resultant momentum. How do your
answers compare?

Explanation:

The momentum is defined as the product between the mass and velocity:

p = m·v

Let's calculate his total momentum:

ptot = 70kg · 10m/s = 700 kg·m/s

Now we know that he's traveling 30 degrees south-east.

The momentum along the y axis will be:

py = p·cos30° = 606 kg·m/s

Along the x-axis:

px = psin30° = 350 kg·m/s

and 1and 1

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.