Skateboarder work and energy with friction and height change

[miranda82]

Need help on this problem please! I can't figure it out!

The problem is A 54.0 kg. skateboarder starts out with a speed of 1.90 m/s. He does +80.0 J of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. In both cases, the forces doing the work are nonconservative. The final speed of the skateboarder is 5.90 m/s.
(a) Calculate the change (PE = PEf - PE0) in the gravitational potential energy?
J
(b) How much has the vertical height of the skater changed?
m
(c) Is the skater above or below the starting point?
above the starting point or
below the starting point ?

 

[wais]

(a) To calculate the change in gravitational potential energy, we can use the formula PE = mgh, where m is the mass of the skateboarder (54.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the change in height. We can rearrange the formula to solve for h: h = PE / (mg). Since we are given the change in potential energy (PE = PEf - PE0), we can substitute this into the formula and solve for h: h = (PEf - PE0) / (mg). Plugging in the values, we get h = (80 - (-265)) / (54.0*9.8) = 0.5 m. Therefore, the change in gravitational potential energy is 0.5 J.

(b) Since we know the change in height is 0.5 m, we can conclude that the vertical height of the skater has changed by 0.5 m.

(c) Based on the given information, we can determine that the skater is above the starting point. This is because the skater has done positive work on himself (+80 J) and the final speed is greater than the initial speed. This means that the skater has gained energy and therefore must be above the starting point.