Physics 111 Summer 2016 HW3
DUE Tuesday, 31 May 2016
GVA-01. A physics professor leaves her house and walks along the sidewalk toward campus. After 5 minutes it starts to rain and she returns home. Her distance from her house as a function of time is shown in the figure at right. At which of the labeled points is her velocity a) zero? b) constant and positive? c) constant and negative? d) increasing in magnitude? e) decreasing in magnitude? (Magnitude refers to the absolute value of the velocity.)
GVA-01A. The graph at right shows the velocity of a particle as a function of time. Assume that it is at x = 0.0 m when t = 0 (in other words, x(0) = 0.0 m).
a) Is the acceleration constant? Explain. If it is, determine the acceleration.
b) Where is the particle when t = 5.0 s?
c) When does the particle stop? Where is it on the x-axis when it does stop?
d) When (for t > 0.0s) does the particle have the same │vx│ that it did for t = 0.0s?
GVA-02. The graph at right describes the acceleration as a function of time for a stone rolling down a hill starting from rest.
a) Find the change in the stone’s velocity between t = 2.5s and t = 7.5 s.
b) Sketch a graph of the stone’s velocity as a function of time.
CA-00. At t = 0, a particle is at x = 5.0 m and has a velocity vx = +10.0 m/s. It undergoes a constant acceleration of -3.0 m/s2.
a) What is the particle’s location when t = 3.0 s?
b) At what value of x does the particle briefly stop and begin to move in the negative x direction?
c) At what time (after t = 0s) does the particle reach x = 5.0 m again?
d) Sketch x(t) and v(t) for 0.0 s £ t £ 10.0 s.
CA-04. (A classic, but mathematically perhaps a little challenging.) The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of -0.100 m/s2, while the freight train continues with constant speed.
a) Will the cows nearby witness a collision? (Well, yes.)
b) If so, where will it take place relative to the place where the freight train was 200m away from the caboose? (You may get two answers. Interpret both.)
c) On a single graph, sketch the positions of the front of the passenger train and the back of the freight train.
CA-06. A model rocket has a constant upward acceleration of 40.0 m/s2 while its engine is running. The rocket is fired vertically, and the engine runs for 2.50 s before it uses up the fuel. After the engine stops, the rocket is in free fall. The motion of the rocket is purely up and down.
a) Sketch the ax vs. t, vx vs. t, and x vs. t graphs for the rocket.
b) What is the maximum height that the rocket reaches?
c) What will the speed of the rocket just before it hits the ground?
2DCA-02. Firemen are shooting a stream of water at a burning building using a high-pressure hose that shoots out the water with a speed of 25.0 m/s as it leaves the end of the hose. Once it leaves the hose, the water moves in projectile motion. The firemen adjust the angle of elevation α of the hose until the water takes 3.00 s to reach a building 45.0 m away. You can ignore air resistance, and assume that the end of the hose is at ground level.
a) Find the angle of elevation α.
b) Find the speed and acceleration of the water at the highest point in its trajectory.
c) How high above the ground does the water strike the building, and how fast is it moving just before it hits the building?
2DCA-03. An airplane is flying with a velocity of 90.0 m/s at an angle of 23.0o above the horizontal. When the plane is 114 m directly above a dog that is standing on level ground, a suitcase drops out of the luggage compartment. How far from the dog will the suitcase land? You may ignore air resistance.
2DCA-05. A baseball thrown at an angle of 60.0o above the horizontal strikes a building 18.0 m away at a point 8.00 m above the point from which it is thrown. Ignore air resistance.
a) Find the magnitude of the initial velocity of the baseball (the velocity with which the baseball is thrown).
b) Find the magnitude and direction of the velocity of the baseball just before it strikes the building.
c) Sketch x vs. t, y vs. t, vx vs t, and vy vs t graphs of the motion.
2DCA-07. A cannon sits at the edge of a vertical cliff that overlooks a flat valley. The nozzle of the cannon is a height h above the valley floor. If the cannon shoots a cannonball horizontally off the cliff with speed vi, derive an expression for the horizontal distance d the ball lands from the cliff wall on the valley floor in terms of vi and h.
(over)