A boulder that can be modeled as a sphere rolls down a hill without slipping. The radius of the boulder is 1 meter, the mass of the boulder is 200 kg. The boulder started from rest and rolls 100 meters down the surface of the hill which has a constant slope of 15 degrees. 1. What is the speed of the boulder just as it reaches the bottom of the hill?

A motorsports driver is driving his car at a constant speed of 37.0 m/s on a circular track with a radius of 260 m. What is the angular speed (in rad/s) of the car? What are the magnitude (in m/s2) and direction of the car's acceleration?

Hello, Can someone please show how to solve this problem? Thanks

Merry-go-rounds are a common ride in park playgrounds. The ride is a horizontal disk that rotates about a vertical axis at their center. A rider sits at the outer edge of the disk and holds onto a metal bar while someone pushes on the ride to make it rotate. Suppose that a typical time for one rotation is 6.0 ss and the diameter of the ride is 16 ftft . 1. For this typical time, what is the speed of the rider, in m/sm/s? Express your answer in meters per second. 2. What is the rider’s radial acceleration, in m/s2m/s2? Express your answer in meters per second squared. 3.  What is the rider’s radial acceleration if the time for one rotation is halved? Express your answer in meters per second squared.