A boat starts out on one bank of a river and heads directly across the river at a constant velocity of 5 m/s relative to the water. The river flows with a uniform velocity of 3 m/s. The river is 75 m wide. How far downstream from the original position does the boat cover while crossing to the opposite bank of the river

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

A1-lb collar is attached to a spring and slides without friction along a circular rod in a vertical plane. the spring has an undeformed length of 5 in. and a constant k =25 lb/ft. knowing that the collar is released from being held at a determine, the speed of the collar and the normal force between the collar and the rod as the collar passes through b.

When a pendulum is held high and taut and then is released, the pendulum begins to swing. what’s the correct order of the energy transformations in this example? (pe stands for potential energy.)