A55.6-kg skateboarder starts out with a speed of 2.44 m/s. he does 80.4 j of work on himself by pushing with his feet against the ground. in addition, friction does -244 j of work on him. in both cases, the forces doing the work are non-conservative. the final speed of the skateboarder is 7.24 m/s. (a) calculate the change (pef - pe0) in the gravitational potential energy. (b) how much has the vertical height of the skater changed? give the absolute value.

(a) -1620.8 J

The initial kinetic energy of the  skateboarder is:

where m is the skateboarder's mass and u his initial speed;

While the final kinetic energy is

where v is his final speed.

So the change in kinetic energy is

According to the work-energy theorem, the change in mechanical energy (kinetic+potential) of the skateboarder is equal to the work done on it:

where

is the work done by the skateboarder on himself

is the work done by friction

is the change in gravitational potential energy

Solving for ,

(b) 2.97 m

The change in potential energy of the skateboarder can be written as

where

m = 55.6 kg is the mass

g = 9.8 m/s^2 is the acceleration of gravity

is the change in vertical height of the skateboarder

Solving for ,

Where the negative sign means the skateboarder has moved downwards. Since we are interested only in the absolute value, the answer is

h = 2.97 m

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.