One game at the amusement park has you push a puck up a...

One game at the amusement park has you push a puck up a long, frictionless ramp. You win a stuffed animal if the puck, at its highest point, comes to within $10 \mathrm{~cm}$ of the end of the ramp without going off. You give the puck a push, releasing it with a speed of $5.0 \mathrm{~m} / \mathrm{s}$ when it is $8.5 \mathrm{~m}$ from the end of the ramp. The puck's speed after traveling $3.0 \mathrm{~m}$ is $4.0 \mathrm{~m} / \mathrm{s}$. Are you a winner?

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Key Concepts

Frictionless Motion

Frictionless motion refers to an idealized scenario where no energy is lost due to friction or air resistance. This assumption simplifies the analysis of systems by ensuring that energy is conserved and only transformed between kinetic and potential forms.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. In problems involving frictionless motion, a decrease in kinetic energy directly corresponds to an increase in gravitational potential energy as an object ascends, and vice versa.

Conservation of Mechanical Energy

This principle states that in the absence of external non-conservative forces (like friction), the total mechanical energy (the sum of kinetic and potential energies) of a system remains constant. It allows one to relate changes in an object's speed to its change in height or position within a gravitational field.

Gravitational Potential Energy

Gravitational potential energy is the energy an object has due to its position relative to a gravitational source, typically measured by its height. When an object moves upward against gravity in a frictionless environment, its kinetic energy is converted into gravitational potential energy.

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