Homework assignment for one dimensional kinematics, physics 4A

1. A dog sees a flowerpot sail up and then back past a window H high. If the total time the pot is in sight is t seconds, find the height above the window that the pot rises.
    (Let H = 2 m and t = 1.0 s, find the height above the window-- after you have found an algebraic solution.)

2. An elevator ascends with an upward acceleration of a. At the instant its upward speed is v, a loose bolt drops from the ceiling of the elevator distance d 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 a distance d below. The drops fall at regular intervals of time, the first drop strikes 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. 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?



6.  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?

7.  If a body travels half its total path in the last second of its fall from rest, find
   a.  the time and
    b.  the height of its fall

8.  A load of bricks is being lifted by a crane at the steady velocity of Vo when one brick falls of H 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 long does it take to reach the ground?
    c.  What is its speed just before it hits the ground?

9.  Ball A is dropped from the top of a building at the 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?  

10.  A train starts from a station with a constant acceleration of at.  A passenger arrives at the track time t1 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 passenger and the train as functions of time.

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