A snowboarder with a mass of 57 kg starts from rest at the top of africtionless slop at a height of45 m. She follows the frictionless path shownin figure. Calculate her speed at the second peak?
Question
A snowboarder with a mass of 57 kg starts from rest at the top of africtionless slop at a height of45 m. She follows the frictionless path shownin figure. Calculate her speed at the second peak?
Solution
To solve this problem, we can use the principle of conservation of energy. This principle states that the total energy in a closed system remains constant. In this case, the snowboarder's total energy is the sum of her potential energy (due to her height) and her kinetic energy (due to her speed).
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First, we calculate the potential energy at the top of the slope. The formula for potential energy is PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height.
PE = (57 kg) * (9.8 m/s²) * (45 m) = 25,074 Joules
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At the second peak, the snowboarder's potential energy is converted into kinetic energy. The formula for kinetic energy is KE = 1/2 mv², where m is mass and v is speed.
Since the total energy remains constant, the kinetic energy at the second peak is equal to the potential energy at the top of the slope.
25,074 Joules = 1/2 * (57 kg) * v²
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Solving for v, we get:
v² = (2 * 25,074 Joules) / (57 kg)
v² = 880.49 m²/s²
v = sqrt(880.49 m²/s²) = 29.67 m/s
So, the snowboarder's speed at the second peak is approximately 29.67 m/s.
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