Homework assignment set one for one dimensional kinematics, physics 4A.

1. A dog sees a flowerpot sail up and then back past a window 5.0 ft high. If the total time the pot is in sight is 1.0 seconds, find the height above the window that the pot rises.

2. An elevator ascends with an upward acceleration of 4.0 ft/s2. At the instant its upward speed is 8.0 ft/s, a loose bolt drops from the ceiling of the elevator 9.0 ft from the floor. Calculate:
a. the time of flight of the bolt from ceiling to floor.
b. the distance it has fallen relative to the elevator shaft.

3. Water drops from the nozzle of a shower onto the floor 81 inches below. The drops fall at regular intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall. Find the location of the individual drops when a drop strikes the floor.

4. Two bodies begin a free fall from rest from the same height 1.0 seconds apart. How long after the first body begins to fall will the two bodies be 10 m apart?

5.  It has been found that galaxies are moving away from the Milky Way (i.e., the Earth) at a speed that is proportional to their distance from the earth. This discovery is known as Hubble's law. The speed of a galaxy a distance r  away is given by: V = Hr, where H is Hubble's constant, which is about
2.33 X 10 -18 s^-1. What is the speed of a galaxy 5 X 1022 m from the Milky Way and 2 X 1025 m from the Milky Way?
THE REAL QUESTION IS THIS: If each of these galaxies has traveled with constant speed, how long ago were they both located at the same place as the Milky Way? (see http://en.wikipedia.org/wiki/Hubble%27s_law)

6.  At the instant the traffic light turns green, an automobile starts with a constant accelerations s of 6.0 ft/s2. At the same instant a truck, traveling with a constant speed of 30 ft/s, overtakes and passes the automobile.
a. How far beyond the starting point will the automobile overtake the truck?
b. How fast will the car be traveling at that instant?

7. Two balls are thrown from the top of a building a distance H from the ground.  One ball is thrown vertically up with initial velocity V, while the other is thrown vertically down with velocity V.  
    a.  How long does it take the ball thrown upward to get to its highest point?
    b.  How high does it rise?  
    c.  What is the difference in the time of flights for the two balls?
        (Let H = 3 m, V = 24 m/s)

8.  A speeding motorist traveling with velocity Vm  is spotted by a police car.  The police car is initially at rest, but the instant the motorist passes, accelerates with constant acceleration ap.  Assume the police car maintains this acceleration and the motorist maintains velocity Vm.  Find:
   a.  The velocity of the police car when it catches up to  the motorist.
   b.  The time it takes for the police car to catch the motorist.
   c.  How far does the police car travel to catch the motorist?

9.  If a body travels half  its total path in the last second of its fall from rest.
    a.  find the total flight time.
    b.  find the height from which it fell.

10.  A load of bricks is being lifted by a crane at the steady velocity of Vo = 5 m/s  when one brick falls of H = 5m above the ground.  Describe the motion of the free brick by sketching x(t).  
    a.  What is the greatest height above the ground that the brick reaches?
    b.  How much time does it take to reach the ground?
    c.  What is its speed just before it hits the ground?

11.  Ball A is dropped from the top of a building a thte same instant that ball B is thrown vertically upward from the ground.  When the balls collide, they are moving in opposite directions, and the speed of A is twice the speed of B.  At what fraction of the height of the building does the collision occur? 

12.  A train starts from a station with a constant acceleration of at = 0.40 m/s2.  A passenger arrives at the track time t = 6.0s after the end of the train left the very same point.  What is the slowest constant speed at which she can run and catch the train.  Sketch curves for the motion of the pasenger and the train as functions of time.