An 80 kg skateboarder going 10 m / s is launched nearly vertically off a ramp as shown. Approximately how high does he go?
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To determine how high the skateboarder goes, we need to consider the principles of energy conservation. The initial energy of the skateboarder consists of both kinetic energy and potential energy. As the skateboarder reaches the maximum height, all of the initial kinetic energy is converted into potential energy.
First, let's calculate the initial kinetic energy of the skateboarder using the formula:
Kinetic Energy = 0.5 * mass * velocity^2
Given:
Mass (m) = 80 kg
Velocity (v) = 10 m/s
Plugging in the values, we get:
Kinetic Energy = 0.5 * 80 kg * (10 m/s)^2
= 0.5 * 80 kg * 100 m^2/s^2
= 4000 J
Next, we know that the potential energy at the maximum height is equal to the initial kinetic energy. Using the formula for potential energy:
Potential Energy = mass * gravitational acceleration * height
Gravitational acceleration (g) is approximately 9.8 m/s^2, and we need to solve for height. Rearranging the formula, we get:
Height = Potential Energy / (mass * gravitational acceleration)
Plugging in the values, we have:
Height = 4000 J / (80 kg * 9.8 m/s^2)
= 5.102 m
Therefore, the skateboarder reaches approximately 5.102 meters in height.