hw2_sol_sp10

# hw2_sol_sp10 - Physics 101 Classical Physics Spring 2010...

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Unformatted text preview: Physics 101 Classical Physics Spring 2010 Homework 2 Solutions DUE IN CLASS ON JANUARY 28 1. A ball is released from rest and falls a distance h under the influence of gravity. What is its average speed during the fall? (a) r 1 2 gh , (b) 1 2 √ gh , (c) √ 2 gh , (d) √ gh , (e) 2 √ gh 0 = h- 1 2 gt 2 ⇒ t = s 2 h g ⇒ Δ x Δ t = h p 2 h/g = r 1 2 gh 2. A vector ~ A = 6 ˆ i is added to a vector ˆ B =- 8 ˆ j . Their sum ~ C = ~ A + ~ B is: (a) 14 ˆ k , (b)- 2 ˆ k , (c) 6 ˆ i + 8 ˆ j , (d)6 ˆ i- 8 ˆ j , (e) -2 3. The smallest the magnitude of the sum of two vectors can be occurs when: (a) The vectors are identical, (b) The vectors point in the same direction, (c) The vectors are perpendicular to each other, (d) There is an angle of 45 ◦ between them (e) They point in opposite directions 4. A vector of magnitude 10 is added to another of magnitude 15. The magnitude of this sum can be: (a) 0, (b) 35, (c) 3, (d) 12 , (e) 50 The magnitude must be greater than 5 (vectors point in opposite directions) and less than 25 (vectors point in same direction). 5. Which of the following is a scalar quanity? (a) velocity, (b) displacement, (c) mass , (d) acceleration, (e) none of these 1 6. A vector A has a magnitude of 5.0 and has an angle of 60 ◦ with respect to the horizontal positive x-axis, measuring counter-clockwise from that axis. Vector B has a magnitude of 10.0 and makes an angle of 60 ◦ with the vertical positive y-axis, measuring clockwise from that axis. What vector represents the sum of the two vectors, using the notation where ˆ i is the unit vector in the postive x direction, and ˆ j is the unit vector in the positive y direction? Referencing both angles from the positive x-axis and adding the components separately, ~ A = 5cos(60 ◦ ) ˆ i + 5sin(60 ◦ ) ˆ j = 5 2 ˆ i + 5 √ 3 2 ˆ j ~ B = 10cos(30 ◦ ) ˆ i + 10sin(30 ◦ ) ˆ j = 5 √ 3 ˆ i + 5 ˆ j ⇒ ~ A + ~ B = ( 5 2 + 5 √ 3 ) ˆ i + 5 √ 3 2 + 5 ˆ j = 5 2 (1 + 2 √ 3) ˆ i + 5 2 (2 + √ 3) ˆ j 7. Use the following figure and information for the next 4 questions. As shown in the figure, a vector A makes an angle θ with the y-axis of a rotated...
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hw2_sol_sp10 - Physics 101 Classical Physics Spring 2010...

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