Final answer:
To graph the gravitational potential energy (GPE) vs height every 2m as the student goes down the slide, we need to calculate the GPE at different heights using the formula GPE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. We can then plot these values on a graph to show the relationship between GPE and height.
Step-by-step explanation:
To graph GPE vs height every 2 m as the student goes down the slide, we need to calculate the GPE at different heights. The formula for gravitational potential energy (GPE) is GPE = mgh, where m is the mass in kg, g ≈ 10 m/s² is the acceleration due to gravity, and h is the height in meters. In this case, the student's weight is given as 300 N, which can be converted to mass using the formula w = mg, where w is the weight and g is the acceleration due to gravity. Therefore, m = w/g = 300 N / 10 m/s² = 30 kg.
Now, we can calculate the GPE at different heights:
At the top of the slide: h = 3 m, GPE = mgh = 30 kg * 10 m/s² * 3 m = 900 J
2 m down the slide: h = 1 m, GPE = mgh = 30 kg * 10 m/s² * 1 m = 300 J
4 m down the slide: h = -1 m (height above ground is negative), GPE = mgh = 30 kg * 10 m/s² * -1 m = -300 J
6 m down the slide: h = -3 m, GPE = mgh = 30 kg * 10 m/s² * -3 m = -900 J
Plotting these values on a graph, with GPE in joules on the x-axis and height in meters above ground on the y-axis, we would have the following points: (900, 3), (300, 1), (-300, -1), (-900, -3). Connecting these points with a line would show the relationship between GPE and height as the student goes down the slide.