Aplane is traveling at north east direction, 30° regard to the north. if not wind it could travel at 60 m/s but it results that there is wind going to the east at 20 m/s. determine the resulting speed of the plane regard to earth.

Speed of the plane regard to earth= 72.1110 m/s

Explanation:

First we decompose the plane's velocity on the horizontal and vertical X-axis, taking into account the deviation of the direction of the plane 30 ° with respect to the north to the east:

Vx= (60m/s) × sen(30°)= 30 m/s

Vy= (60m/s) × cos(30°)= 59.9615m/s

The wind speed only has component in the horizontal X axis since it has east direction:

Vx= 20 m/s

We add the components of the wind on the X axis and then the components on the Y axis to be able to determine the resulting velocity using the Pythagorean theorem, taking as the hypotenuse result and the X and Y components the catheters. This result will be the final speed of the plane with respect to Earth:

Vx= (20m/s) + (30m/s)= 50m/s

Vy= 59.9615m/s

V= √( (50m/s)² + (59.9615m/s)² )= 72.1110m/s

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.