A 4.0 kg mass stone is thrown vertically upwards at a speed of 20 m/s. I) determine the maximum height it reaches.
II) Determine your speed when in the
half of its maximum height.
III) Determine the total mechanical energy at this point. of
work performed by the gravitational force from the launch point to the return to that point.

Acertain radio station broadcasts radio waves that have a wavelength of 298cm what is its broadcast frequency?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

Asled is being held at rest on a slope that makes an angle θ with the horizontal. after the sled is released, it slidesa distance d1 down the slope and then covers the distance d2 alongthe horizontal terrain before stopping. find the coefficient ofkinetic friction μk between the sled and the ground, assumingthat it is constant throughout the trip. find the coefficient of kinetic frictionμk. express your answer in terms of someor all of the variables d1, d2, and θ.