A 60.8-kg skateboarder starts out with a speed of 1.84 m/s. He does 90.8 J of work on himself by pushing with his feet against the ground. In addition, friction does -278 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 8.12 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.

I have calculated the PE and found it to be -2088.69J. However, I am stuck on trying to solve part b. Please help!

http://www.jiskha.com/display.cgi?id=1429748458

well we agree on part a and part b is easy

To calculate the change in gravitational potential energy (ΔPE) and the change in vertical height, we can use the formulas:

ΔPE = PEf - PE0
ΔPE = m * g * Δh

where m represents the mass of the skateboarder, g is the acceleration due to gravity, and Δh represents the change in vertical height.

We already have the value for ΔPE, which is -2088.69 J. Now, let's calculate Δh:

ΔPE = m * g * Δh

Since the mass of the skateboarder is given as 60.8 kg, we can use this value. However, the value for g (acceleration due to gravity) is not provided in the question. Typically, on Earth, the approximate value for g is 9.8 m/s².

Substituting the values we know into the equation:

-2088.69 J = 60.8 kg * 9.8 m/s² * Δh

Now, let's solve the equation for Δh:

Δh = -2088.69 J / (60.8 kg * 9.8 m/s²)
Δh ≈ -3.39 meters

The absolute value of Δh gives the magnitude of the change in vertical height, so:

|Δh| ≈ 3.39 meters

Therefore, the vertical height of the skater has changed by approximately 3.39 meters.