Solve the following problems on a separate sheet of paper. Be mindful to follow established problem-solving format, showing all work, equations, substitutions, and units. Freely consult your class textbook and your Reference Tables for Physics. [KE refers to Mechanical Kinetic Energy and PE refers to Gravitational Potential Energy in this exercise.]

1. A 20.00 kilogram bowling ball is at rest on the very edge of a shelf. The shelf is situated 10.00 meters above a horizontal floor. The ball is given a negligible push and begins its descent to the floor.

(A) Calculate the PE and KE of the bowling ball at rest on the shelf.

(B) Calculate the PE and KE of the bowling ball just at the moment of impact at the floor.

(C) Calculate the impact speed of the bowling ball.

(D) Calculate the travel time of the bowling ball from the shelf to the floor.

2. A 0.2 kilogram baseball is thrown vertically downwards towards to the same horizontal floor in Problem 1. The baseball possesses an initial velocity of 30 meters per second. The ball just so happens to leave the hand of the thrower at the same distance above the floor as the bowling ball in the previous problem.

(A) Calculate the PE and KE of the baseball at the moment of release from the thrower's hand.

(B) Calculate the PE and KE of the baseball at the moment of impact at the floor.

(C) Calculate the impact speed of the baseball.

(D) Calculate the travel time of the baseball from the thrower's hand to the floor.

3. A rocket car is traveling on a linear horizontal frictionless track when it suddenly runs out of fuel. The car has achieved a speed of 100 meters per second at the very moment the fuel is completely spent. The track then suddenly changes to a 30-degree incline from the horizontal.

(A) Calculate the maximum height above the horizontal track the car will rise just as it comes to a complete stop.

(B) Calculate the distance, measured along the inclined track, the car will travel before coming to a complete stop.

(C) Calculate the total travel time of the car on the inclined plane from the time it enters the track to the time it comes to a complete stop on the inclined track.

(D) Calculate the rate of deceleration of the car on the inclined track.

4. A 7.00-kilogram rock at initially at rest suddenly begins to descend from the cliff to which it was attached. The rock strikes the ground exactly 4.00 seconds later.

(A) Calculate the PE and KE of the rock at the very start of its descent.

(B) Calculate the PE and KE of the rock at the moment of impact at the base of the cliff.

(C) Create a table of PE and KE values for the rock at 1.00-second intervals from the start of its descent to the base of the cliff.

(D) Prepare a graph of PE (y-axis) versus KE (x-axis) for the rock's descent. Briefly characterize the observed relationship between the PE and KE of the rock during its descent.