Question

A roller coaster starts with a speed of 15.0 m/s at a point 45 m above the bottom of a dip. Neglecting friction, what will be the speed of the roller coaster at the top of the next slope, which is 30 m above the bottom of the dip?

Answer 1

The speed of the roller coaster at the top of the next slope, neglecting friction, will be approximately 29.74 m/s.

Step-by-step explanation:

To find the speed of the roller coaster at the top of the next slope, we can use the concept of conservation of mechanical energy. At the top of the first slope, the roller coaster has potential energy given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. At the bottom of the first slope, all the potential energy is converted to kinetic energy, given by the equation KE = 0.5mv^2, where v is the velocity. Since there is no friction, the mechanical energy is conserved, so the potential energy at the top of the second slope is equal to the kinetic energy at the bottom of the first slope. Therefore, we can equate the two equations: mgh1 = 0.5mv^2, where h1 is the height of the first slope and v is the velocity at the top of the second slope. Solving for v, we get:

v = sqrt(2gh1)

Substituting the given values, we have:

v = sqrt(2 * 9.8 m/s^2 * 45 m)

v ≈ 29.74 m/s