1) A rock A dropped from the top of a vertical cliff and takes 3.00 s to reach the ground below the cliff. A second rock is thrown vertically from the cliff, and it takes this rock 2.00 s to reach the ground below the cliff from the time it is released. With what velocity was the second rock thrown, assuming no air resistance?
2) In a medical X-ray tube, electrons are accelerated to a velocity of vf and then slammed into a tungsten target. As they stop, the electrons' rapid acceleration produces X rays. If the time for A electron to stop is time tf, approximately how far does it move while stopping? Express your answer in terms of vf and tf.
3) To determine the height of a flagpole, Abby throws a ball straight up and times it. She sees that the ball goes by the top of the pole after 0.5 s and then reaches the top of the flagpole again after a total elapsed time of 4.1 s. How high is the pole above the point where the ball was launched? (You can ignore air resistance.) Hint draw a position vs. time graph.
4) Speedy Sue, driving at 30.0 m/s, enter a one-lane tunnel. She then observes a slow-moving ven 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at -2.00 m/s2 because the road is wet. Will there be a collision? If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of clAest approach between Sue's car and the van.
5) A man A running et speed. c (much less than the speed of light) to catch a bus ahflady at a stop. At t = 0, when he it a distance b from the door of the bus, the bus sticts moving with the positive acceleration a. Use a coordinate system with x = 0 at the door of the stopped bus.
(a) Draw a position vs. time graph for both the man and bus on the same graph. Make sure to label what object each curve corresponds to and the initial position of each object A the graph.
(b) What is xman(t), the position of the man as a function of time.
(c) What is xbus(t), the position of the bus as a function of time.
(d) What condition is vecesary for the man to catch the bus? Assume he catches it at the time tcatch. Hint When are the bus and person at the same position at the same time?
(e) Find the minimum speed, cmin that the man needs to catch the bus.
(f) Assume that the man misses getting aboard when he first meets up with the bus Does he get a second chance if he conWnues to run at the constant speed c > cmin? Explain.
6) A person launch. a home built rocket straight up into the ar. At t = 0 the rocket is at rest at y = 0 with vo = 0. The position of the rocket W given by
y(t)=1/2(a-g)t2 - ao/30to4(t6), 0< t < to
where ao is a positive constant and g is the acceleration of gravity. to is the time that it takes the fuel to burn out.
(a) Find the expressions for the velocity and acceleration as a function of time.
(b) Make a graph of the acceleration vs. time and velocity vs. time. For your graphs you can use:
ao = 40 m . s-2, g = 10 m • s-2 , to = 2s
(c) Show that your expressions for the velocity and acceleration you found in part (b) are dimensonally correct when using the values stated in past (c).