Homework #1 Physics 111-4 Spring 2012 Page 1 of 2
Homework #1
Chapter 2: Motion in a Straight Line
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#1: Under what conditions are average and instantaneous velocity equal?
#9. In which of the velocity versus time graphs would the average velocity over the interval shown equal the average of the velocities at the ends of the interval?
#13: The standard 26-mile, 385 yard marathon dates to 1908, when the Olympic marathon started at Windsor Castle and finished before the Royal Box at London’s Olympic Stadium. Today’s top marathoners achieve times around 2 hours, 4 minutes for the standard marathon. (a) What’s the average speed of a marathon run in this time? (b) Marathons before 1908 were typically about 25 miles. How much longer does the race last today, assuming as a result of the extra mile and 385 yards, assuming it’s run at the average speed?
#17: Taking Earth’s orbit to be a circle of radius 1.5x108 km, determine the Earth’s orbital speed in (a) meters per second and (b) miles per second.
#21: A model rocket is launched straight upward. Its altitude y as a function of time is given by y=bt-ct2, where b=82 m/s, c=4.9 m/s2, t is time in seconds, and y is in meters. (a) Use differentiation to find a general expression for the rocket’s velocity as a function of time. (b) When is the velocity zero?
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#26: An airplane’s takeoff speed is 320 km/hr. If it’s average acceleration is 2.9 m/s2, how much time is it accelerating down the runway before it lifts off?
#34: In a medical x-ray tube, electrons are accelerated to a velocity of 108m/s and then slammed into a tungsten target. As they stop, the electrons’ rapid acceleration produces x-rays. If the time for an electron to stop is on the order of 10-9s, approximately how far does it move while stopping?
#42: Space pirates kidnap an earthling and hold him on one of the planets in the solar system. With nothing else to do, the prisoner amuses himself by dropping his watch from eye level (170cm) to the floor. He observes that the watch takes 0.95s to fall. On which planet is he being held? (Use appendix E to help you!)
Chapter 3: Motion in Two and Three Dimensions
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#1: Under what conditions is the magnitude of the vector sum A+ B equal to the sum of the magnitudes of the two vectors?
#4: Can an object have southward acceleration while moving northward? A westward acceleration while moving northward?
#12. An ion in a mass spectrometer follows a semicircular path with a radius 15.2cm. What are (a) the distance it travels and (b) the magnitude of its displacement?
#21: An object’s velocity is v=ct3i+ dj, where t is time and c and d are positive constants with appropriate units. What’s the direction of the object’s acceleration?
#27: You wish to row straight across a 63m wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 0.57m/s. (a) What direction should you head? (b) How long will it take you to cross the river?
#33: A carpenter tosses a shingle horizontally off an 8.8m high roof at 11 m/s. (a) How long does it take the shingle to reach the ground? (b) How far does it move horizontally?
#35: Droplets in an ink-jet printer are ejected horizontally at 12 m/s and travel a horizontal distance of 1.0mm to the paper. How far do they fall in this interval?
#39: Estimate the acceleration of the moon, which completes a nearly circular orbit of 385,000km radius every 27 days.