PHYS.1410 Physics I Exam 1 Spring 2016 (version A)

Transcription

1 PHYS.1410 Physics I Exam 1 Spring 016 (version A) Recitation Section Number Name (PRINT) / LAST FIRST Last 3 Digits of Student ID Number: Fill out the above section of this page and print your last name on the top of each of the following pages of the exam. The last page of the exam is a formula sheet. You may carefully remove it. (At the end of the exam please take it with you or throw it in a waste basket!) Be prepared to show your Student ID Card. Answer all questions, beginning each new question in the space provided. Show all work. Show all formulas used for each problem prior to substitution of numbers. Label diagrams and include appropriate units for your answers. You may NOT use anything other than a hand-held calculator to assist in doing numerical calculations. Score on each problem: I. (5) II. (5) III. (5) IV. (5) Total Score (max. = 100 pts)

2 Part I. (5 points each) Put a circle around the letter that represents the best answer. I-1 The figure shows the graph of the position x as a function of time t for an object moving in the straight line (the x-axis). Which of the following graphs best describes the velocity along the x-axis as a function of time for this object? A) B) C) D) E) I- Joy and Faith dive from an overhang into the lake below. Joy simply drops straight down from the edge. Faith takes a running start and jumps with an initial horizontal velocity of 5 m/s. When they reach the lake below, the following statement is correct. A) The splashdown speed of Joy is larger than that of Faith. B) The splashdown speed of Faith is larger than that of Joy. C) They will both have the same splashdown speed. D) The splashdown speed of Joy will always be 9.8 m/s larger than that of Faith. E) The splashdown speed of Faith will always be 5 m/s larger than that of Joy. I-3 Two objects are thrown from the top of a tall building. One is thrown up, and the other is thrown down, both with the same initial speed (neglect air resistance). What are their speeds when they hit the street? A) The one thrown up is traveling faster. B) The one thrown down is traveling faster. C) They are traveling at the same speed. D) It is impossible to tell because the height of the building is not given. E) It is impossible to tell because a numerical value for the initial speed is not given.

3 3 Part I - continued Put a circle around the letter that represents the best answer. I-4 Which of the following is an accurate statement? A) The magnitude of a vector can be zero even though one of its components is not zero. B) It is possible to add a scalar quantity to a vector. C) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero. D) Rotating a vector about an axis passing through the tip of the vector does not change the vector. E) The magnitude of a vector is independent of the coordinate system used. I-5 Shown below are the velocity and acceleration vectors for a person in several different types of motion. In which case is the person slowing down and turning to his right? A) B) C) D) E)

4 4 Part II (5 points each part) A car is speeding at 40 m/s as it passes a truck traveling at 5 m/s. Just as the car is along side of the truck, (time t = 0, position x = 0) the driver of the car notices a police car up ahead and brakes at a constant rate of 5 m/s. The truck catches up to the car at time t = t 1 and position x = x 1. A) Draw and label a motion diagram for the car and separately for the truck. B) Draw and label the velocity versus time graph for the car and the truck. C) Draw and label the position versus time graph for the car and the truck. D) Determine the time that the car and the truck have the same speed. E) Determine the time that the truck catches up to the car.

5 5 Part III (5 points each part) A particle undergoes motion with non-uniform acceleration. Its velocity is given by: ˆ v= (6 14 ti ) + (1t 1 t) j ˆ (velocity in m/s, t in seconds) A) Determine the vector components of the velocity at 3 seconds. B) Determine the magnitude and direction of the velocity at 3 seconds. C) Draw and label the velocity vector at 3 seconds. D) Determine the acceleration of the particle as a function of time. E) Determine the vector components of the acceleration at 3 seconds.

6 Part IV (5 points each part) 6 An object is projected from the ground so that it lands at the edge of a cliff that has a height (H) above the ground. The object is in the air for 4 seconds, has an initial speed of the object is 30 m/s, and it launched with an initial angle of 60 degrees above the horizontal. A) Draw and label a diagram of the physical situation (include the trajectory). B) Determine the height (H) of the cliff. C) Determine the horizontal distance that the cliff is from the location where the object is projected. D) Determine the maximum height that the object reaches. E) Determine the impact speed of the object when it hits the cliff.

7 Formulae for Exam #1 Spring Graphical Analysis v a v a avg avg inst inst r = t v = t dr = dt dv = = dt r = r r (slope of position versus time) f i (slope of velocity versus time) (slope of position versus time at a specific time) d r dt (slope of velocity versus time at a specific time) t = t t f i Sf = Si + area under velocity versus time for Δt = tf - ti Vfs = Vis + area under acceleration versus time for Δt = tf - ti Analytical Analysis (for constant linear acceleration) S 1 f = Si + vis + t as t vfs = vis + as t v = v + a S fs is S ( )