Final answer:
To find the minimum speed of a hockey puck to reach the top of a frictionless ramp, we use energy conservation principles and the sine function to calculate the potential energy at the top and equate it to the kinetic energy at the bottom.
Step-by-step explanation:
The student is asking about the minimum speed a hockey puck needs in order to make it to the top of a frictionless ramp. To solve this, we must consider the principles of conservation of energy and kinematic equations from classical mechanics, which is a branch of physics. The hockey puck needs sufficient kinetic energy to overcome the potential energy at the top of the ramp. The potential energy at the top can be calculated by PE = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (approximately 9.81 m/s2), and h is the height of the ramp.
To find the height h of the ramp, we can use the sine function since the ramp makes a 25.0-degree angle with the horizontal, which gives us h = L sin(\theta), where L is the length of the ramp. With the height calculated, we plug the values into PE = mgh to get the potential energy at the top. The kinetic energy KE at the bottom of the ramp must be equal to this potential energy, so KE = (1/2)mv2 where v is the velocity we want to find. Setting these equal gives us the equation (1/2)mv2 = mgh which simplifies to v2 = 2gh. Taking the square root gives us the minimum speed v.
This task requires understanding of projectile motion, force, momentum, and energy conservation, which are all fundamental physics concepts covered in typical high school curricula.