PHYS171_f11_exam_1_solution

PHYS171_f11_exam_1_solution - PHYS171 Name: _ Exam 1 Fall...

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PHYS171 Exam 1 Fall 2011 Name: _____________________ Student ID #: ________ Short Answer Questions 1) If the position of a particle as a function of time is given by 5 s m 3 s m 5 3 3 7 ) ( t t t x = find the acceleration at t = 5 s (5 points) This is not a case of constant acceleration, so we must use calculus. () 5 5 3 5 3 5 3 5 3 s m 3 s m 1 s m 4 s m 2 s m 4 s m 2 s m 5 s m 3 s m 7710 60 42 15 21 15 21 3 7 = = = = = t t t t dt d a t t t t dt d v 2) Sketch the motion for an elevator making a trip from the third floor to the eighth floor of a building. Sketch the position and velocity and acceleration as a function of time from the moment the doors close on the third floor to the moment they open on the eighth floor. (You will not be able to assign numbers to the curve, but make sure the curves have the right slope and curvature.) [5 points] 3) You drop a rock from a window and see it strike the ground 3.2 seconds later with uncertainty 0.1 seconds. Assuming the rock moves with constant acceleration g = 9.805 m/s, what is the height of the window and the uncertainty in the height? [10 points] We use the position equation to find the distance, and error propagation to find the uncertainty. m 2 . 50 ) s 2 . 3 ( s / m 9 . 4 0 0 2 2 2 2 1 2 2 1 0 0 = = + + = + = gt gt t v x x ( ) m 1 . 3 m 1 . 0 .2s 3 s / m 8 . 9 2 t x 2 t 2 2 t 2 2 x = = = = = σ gt gt t x 4) A particle starts at the origin ( j i ˆ 0 ˆ 0 + ) m, travels at constant velocity 1 m/s to the point ( j i ˆ 3 ˆ 0 + ) m then travels at 2 m/s to the point ( j i ˆ 3 ˆ 6 + ) m. What is the average velocity vector and average speed? [5 points] We need to know distance, displacement and time. During the first interval we travel 3 m at 1 m/s, which takes 3 seconds. During the second interval, we travel 6 m at 2 m/s, which also takes 3 seconds. Total time is 6 seconds. speed=(3m + 6m)/6s = 9m/6s = 1.5 m/s velocity = [( j i ˆ 3 ˆ 6 + )m-( j i ˆ 0 ˆ 0 + )m]/6s = ( j i ˆ 5 . 0 ˆ 1 + )m/s time velocity time position
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PHYS171 Exam 1 Fall 2011 Name: _____________________ Student ID #: ________ Problem 1 [30 points] You have a sling-shot that launches a rock at a speed v 0 of exactly 20 meters/second and any angle θ with respect to the horizontal. Launching the rock from ground level, you want to hit an object on the ground which is 25 meters away.
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PHYS171_f11_exam_1_solution - PHYS171 Name: _ Exam 1 Fall...

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