AP Physics C 80pt TAKE HOME TEST over Chapter 3 & 4 9/(21-28)/12 Show your work on problems Box in answers No Naked Numbers!

Transcription

1 AP Physics C 80pt TAKE HOME TEST over Chapter 3 & 4 9/(21-28)/12 Show your work on problems Box in answers No Naked Numbers! name From Homework 1.) A Coast Guard cutter detects an unidentified ship at a distance of 25 miles in the direction 20.0 north of west. This mystery ship is traveling at 26.0 knots on a course at 40.0 south of west. The Coast Guard wishes to send a speedboat to intercept the vessel and investigate it. If the speedboat travels 50.0 km/hr, in what direction should it head to meet it in the shortest amount of time? (1.00 knot = 1.15 mi / hr) required map view drawing: : 2.) A 2.0 m tall (from her feet to her ears) soccer player kicks a rock horizontally off a 50.0 m high cliff into a pool of water. If the player hears the sound of the splash 3.50 sec later, what is the initial speed given to the rock? (speed of sound in air = 343 m/s) 3.) A small Archerfish shoots a ball of water at a bug sitting on a leaf 2.50 m away along a line 20 above the horizontal. With what velocity must the water ball be launched if it is not to drop more than 4.00 cm vertically on its path to the target?

2 4.) A car travels due east with a speed of 60 mi/hr. Raindrops are falling at a constant speed vertically with respect to the earth.. The traces of the rain on the side windows of the car make an angle of 40 with the horizontal. Find the velocity of the rain... a.)... with respect to the car b.)... with respect to the Earth 5.) A basketball player who is 2.20 m tall is standing on the floor 12.0 m from the basket as in the figure below. If he shoots the ball at a 50 angle with the horizontal, at what initial speed must he throw so that it goes through the hoop without striking the backboard? The basket height is 3.05 m. 6.) A train slows down as it rounds a sharp horizontal turn, slowing from km /hr to 50.0 km/hr in the 22 sec that is takes to round the bend. The radius of the curve is 170 m. Compute the acceleration at the moment the train speed reaches 50.0 km/hr. Assume it continues to slow down at this time at the same rate. Draw the train s acceleration vectors on the drawing below: r

3 Chapter 3: Vectors 7.) Use a protractor or at least a ruler for this one. For the following three vectors: Use the head-to-tail construction method to show the resultant of: A + 4.0B C A B C 8.) Add the following three 3D vectors (all with the same origin) using the i, j, k component method: F 1 = S of E 15 below the horizontal ; F 2 = N of W along the horizontal; Attempt a sketch: z F 3 = S of W 30 above the horizontal y x F = ( i + j + k ) N Properly describe the F: F = of the horizontal

4 Chapter 4 Class Notes 9.) Crazy Joe is out to impress his second cousin, Elvira Delborg. He finishes off his 6 pack of Nat Lite and hops on his Kawasaki 400 motorcycle. He guns the engine and drives up and off a ramp then flys through the air over a row of broken down flat bed trucks at the Pawhuska salvage yard. Assuming he takes off and lands at the same level and is airborne for 1.7 seconds, what maximum height above where he left the ramp did he achieve? 10.) Garrett parks his Pontiac Fiero close to a cliff overlooking the ocean. The cliff is on an incline that makes an angle of 25 below the horizontal. Garrett runs to meet his sweetheart, but leaves the car in neutral. The car begins to roll down the incline with a constant acceleration of 1.5 m / s 2 and travels 60.0 m to the edge of the cliff. The cliff s edge is 45.0 m above the ocean. a.) Find the time the car is in the air. b.) Find the position of Garrett s truck relative to the base of the cliff when it lands in the ocean. Complete and label drawing:

5 11.) Derive the formula for centripetal acceleration (a c = v 2 /r) given the following uniform circular motion: Your derivation steps should involve drawings, geometry, algebra and calculus. 12.) Compute the necessary spin rate in rpm (revolutions per minute) about the central symmetry axis of a donut shaped space station 2.1 km in diameter in order to provide a constant simulated 1.0 g environment at the periphery. Show the direction of the acceleration vector on the space station for a person at point A: point A

6 13.) The figure to the right shows the total acceleration (magnitude = 6 m/s/s) vector and instantaneous velocity vector of a particle moving clockwise in a circle of radius 18 m at a given instant of time. At this instant, find:: a.) the radial (centripetal) acceleration and accurately draw it on the fig. b.) the speed of the particle and c.) its tangential acceleration and accurately draw it on the figure.. 14.) What will be the magnitude of the difference in acceleration between these two particles three seconds after they leave the origin? Show your steps. Particle A s position vector: ( r A = 3t 4ˆ i 7t 2 ˆ j ) m Particle B s position vector: ( Sketch their position vectors at 3 seconds (correctly label axes.) y r B = 5t ˆ i + 2t 3 ˆ j ) m x

7 Serway Test Bank /AP Physics C Mech Exam Multiple Choice /University Questions 15.) Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that: a.) it is passing car A. d.) it has the same total acceleration as car A. b. ) it has the same linear (tangential) acceleration as car A. e.) it has traveled farther than car A since starting. c.) it has the same centripetal acceleration as car A. 16.). A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west and the acceleration of the car has components of 2.4 m/s 2 east and 1.8 m/s 2 south. What is the radius of the circle? a.) 0.24 km b.) 0.19 km c.) 0.32 km d.) 0.14 km e.) 0.27 km SHOW ALL WORK ON ALL THESE QUANTITATIVE MULTIPLE CHOICE PROBLEMS FOR FULL CREDIT 17.) At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i 4.0j) m/s 2. At the instant the x coordinate of the particle is 15 m, what is the speed of the particle? a.) 10 m/s b.) 16 m/s c. ) 12 m/s d.) 14 m/s e.) 26 m/s 18.) A carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride? (Assume the passenger is sitting still in the chair.) a ) 5.7 m/s 2 downward b.) 4.1 m/s 2 upward c.) 14 m/s 2 downward d.) 4.1 m/s 2 downward e.) 19 m/s 2 downward 19.) A rock is projected from the edge of the top of a 100-ft tall building at some unknown angle above the horizontal. The rock strikes the ground a horizontal distance of 160 ft from the base of the building 5.0 s after being projected. Assume that the ground is level and that the side of the building is vertical. Determine the speed with which the rock was projected. (remember that g = 32.2 ft/sec/sec) a.) 72 ft/s b.) 77 ft/s c.) 68 ft/s d.) 82 ft/s e.) 87 ft/s