Physics 111121 Vector MiniReview Problem Solutions Contents FOP

Physics 111/121 Vector Mini-Review Problem Solutions Contents FOP FOP 3 -11, 3 -18, 3 -15, 3 -21 5 -6, 5 -7 7 -6, 7 -11 10 -46, 12 -19, 12 -21, 12 -25 1

Problem 3 -11: A woman walks 250 m in the direction 30° east of north, then 175 m directly east. Find (a) the magnitude and (b) the angle of her final displacement from the starting point. (c) Find the distance she walks. (d) Which is greater, that distance or the magnitude of her displacement? 2

Problem 3 -18: Here are two vectors: What are (a) the magnitude and (b) the angle (relative to i ) of a? What are (c) the magnitude and (d) the angle of b ? What are (e) the magnitude and (f) the angle of a + b ; (g) the magnitude and (h) the angle of b - a ; and (i) the magnitude and (j) the angle of a - b ? (k) What is the angle between the directions of b - a and a - b ? 3

Problem 3 -18, continued 4

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Problem 5 -6: Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown in the figure. What is the asteroid's acceleration (a) in unit-vector notation and as (b) a magnitude and (c) a direction? 7

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Problem 7 -6 A floating ice block is pushed through a displacement d = (15 m)i - (12 m)j along a straight embankment by rushing water, which exerts a force F = (210 N)i - (150 N)j on the block. How much work does the force do on the block during the displacement? 9

Prob 7 -11: The figure shows three forces applied to a trunk that moves leftward by 3. 00 m over a frictionless floor. The force magnitudes are F 1 = 5. 00 N, F 2 = 9. 00 N, and F 3 = 3. 00 N. During the displacement, (a) what is the net work done on the trunk by the three forces and (b) does the kinetic energy of the trunk increase or decrease? By how much? 10

Problem 10 -46: Two 2. 0 kg bodies, A and B, collide. The velocities before the collision VA = 15 i + 30 j and v. B = -10 i + 5. 0 j. After the collision, v´A = -5. 0 i + 20 j. All speeds are given in meters per second. (a) What is the final velocity of B? (b) How much kinetic energy is gained or lost in the collision? 11

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