Week 1 Homework Assignment PDF

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Week 1 Homework Assignment

Due Tuesday (Recitation) Week 2

  and 󰇍   1. Given two vectors  (a) Find the magnitude and direction of each vector (b) Write an expression for the vector difference  󰇍 using unit vectors; (c) Find the magnitude and direction of the vector difference  󰇍 (d) In a vector diagram show , 󰇍 and  󰇍 and also show that your diagram agrees qualitatively with your answer in part (c). (e) Find the scalar product  . 󰇍 (f) Find the angle between  and 󰇍 (g) How much of the vector  lies parallel to the vector 󰇍 ? (h) Find the vector product  × 󰇍 (i) How much of the vector  lies perpendicular to the vector 󰇍?

2. A patient with a dislocated shoulder is put into a traction apparatus as shown in the figure. The pulls  and 󰇍 have equal magnitudes and must combine to produce an outward traction force of F on the patient’s arm. How large should these pulls be?

3. A physics professor leaves her house and walks along the sidewalk toward campus. After 5 min it starts to rain and she returns home. Her distance from her house as a function of time is shown in the figure. 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?

4. The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than amax. If you are in an automobile accident with an initial speed vi and you are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

5. George and Harry both can run at speed vr and walk at speed vw, with vw < vr. They set off together on a journey of distance d. George walks half of the distance and runs the second half. Harry walks half of the time and runs the other half. (a) Draw a graph showing the positions of both George and Harry versus time. (b) Write two sentences explaining who wins and why. (c) How long does it take Harry to cover the distance d? (d) Find Harry's average speed for covering the distance d. (e) How long does it take George to cover the distance d?

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