Question

What is the speed of a 1313 kg car on a frictionless rollercoaster as it reaches the peak of a 15.0 m hill if the car starts from rest at a height of 20.0 m?

a) 10.0 m/s
b) 15.0 m/s
c) 20.0 m/s
d) 25.0 m/s

Answer 1

The speed of the car on the frictionless rollercoaster as it reaches the peak of the hill is approximately 19.8 m/s.OPTION C.

Step-by-step explanation:

To find the final speed of the car as it reaches the peak of the hill, we can use the conservation of mechanical energy. At the top of the hill, all of the car's initial potential energy is converted into kinetic energy. The potential energy at the top of the hill can be calculated using the formula PE = mgh, where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the hill.

The initial potential energy is given by PE = (1313 kg)(9.8 m/s^2)(20.0 m) = 256,504 J. This energy is converted into kinetic energy at the top of the hill. The formula for kinetic energy is KE = 0.5mv^2, where m is the mass of the car and v is the final velocity.

So, 256,504 J = 0.5(1313 kg)v^2. Solving for v, we get v^2 = 392 m^2/s^2. Taking the square root, we find v = 19.8 m/s. Therefore, the speed of the car as it reaches the peak of the hill is approximately 19.8 m/s.