Okay, let's solve this step-by-step:
* We are given the mass of the child is 16.0 kg
* The child rolls 2.0 meters down an incline at an angle of 20.0 degrees
* We are told there is no friction, so all the potential energy will be converted to kinetic energy
* Since the child starts at rest, the initial kinetic energy is 0
* The formula for potential energy is: PE = mgh
- Where m is mass, g is acceleration due to gravity (9.8 m/s^2), and h is height
* Since the angle of the incline is 20.0 degrees, we can find the vertical height using trigonometry:
- h = 2.0m * sin(20.0 degrees)
- h = 0.347m
* Now we can find the initial potential energy:
- PE = (16.0kg)*(9.8m/s^2)*(0.347m)
- PE = 56.4 J
* Since all the potential energy is converted to kinetic energy, the final kinetic energy will be 56.4 J.
So the answer is: The kinetic energy of the child at the bottom of the incline is 56.4 Joules.