A car on a roller coaster starts at zero speed at an elevation above the ground of .It coasts down a slope,and then climbs a hill.The top of the hill is at an elevation of .What is the speed of the car at the top of the hill? Neglect any frictional effects.

Question

A car on a roller coaster starts at zero speed at an elevation above the ground of  .It coasts down a slope,and then climbs a hill.The top of the hill is at an elevation of  .What is the speed of the car at the top of the hill? Neglect any frictional effects.

Quizplus · Accepted Answer

According to the law of conservation of energy, the initial potential energy of the car is equal to the sum of its kinetic and potential energies at any point along the path, neglecting any frictional effects.

At the starting point, the potential energy of the car is:
PE = mgh1

where m is the mass of the car, g is the acceleration due to gravity, and h1 is the initial height above the ground.

At the top of the hill, the potential energy of the car is:
PE = mgh2

where h2 is the height of the hill.

At any point along the path, the kinetic energy of the car is given by:
KE = (1/2)mv^2

where v is the speed of the car at that point.

Since the initial speed of the car is zero, the total initial energy of the car is equal to its potential energy at the starting point:

Ei = mgh1

At the top of the hill, the total energy of the car is the sum of its kinetic and potential energies:

Ef = KE + PE = (1/2)mv^2 + mgh2

Since there is no friction, the total energy of the car is conserved and remains constant throughout the motion:

Ei = Ef

Therefore,

mgh1 = (1/2)mv^2 + mgh2

Simplifying and solving for v, we get:

v = sqrt(2gh1-2gh2)

Substituting the given values, we get:

v = sqrt(2*9.81*(11ea83ea_69a4_df91_aeff_0145667f2104_TB6394_11-11ea83ea_69a5_06a2_aeff_dbe22ed628e8_TB6394_11))

v ≈ 14 m/s

Thus, the speed of the car at the top of the hill is approximately 14 m/s. Therefore, the best choice is A).

A Car on a Roller Coaster Starts at Zero Speed