4 - homework 04 KERR, KELSEY Due: Jan 28 2008, 11:00 pm...

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homework 04 – KERR, KELSEY – Due: Jan 28 2008, 11:00 pm 1 Question 1, chap 3, sect 3. part 1 of 2 10 points A boy runs 12 . 7 blocks North, 12 blocks Northeast, and 7 . 6 blocks West. Determine the length of the displacement vector that goes from the starting point to his Fnal position. Correct answer: 21 . 2038 (tolerance ± 1 %). Explanation: Let ˆ ı = East and ˆ = North. The displace- ment vector is v R = 12 . 7 ˆ + 12cos 45 ˆ ı + 12sin 45 ˆ 7 . 6 ˆ ı = R e ˆ ı + R n ˆ  . The length of v R is | v R | = r R 2 e + R 2 n = r (12cos 45 7 . 6) 2 + (12 . 7 + 12sin 45 ) 2 = 21 . 2038 . Question 2, chap 3, sect 3. part 2 of 2 10 points Determine the direction of the displacement vector. (Use counterclockwise as the posi- tive angular direction, between the limits of 180 and +180 from East) Correct answer: 87 . 6072 (tolerance ± 1 %). Explanation: The reference angle is θ = arctan v v v v R n R e v v v v = 87 . 6072 . Since the displacement vector lies in quad- rant 1, the angle is 0 + 87 . 6072 = 87 . 6072 . Question 3, chap 3, sect 1. part 1 of 2 10 points A football player runs directly down the Feld for 44 m before turning to the right at an angle of 19 from his original direction and running an additional 18 m before being tackled. a) What is the magnitude of the runner’s total displacement? Correct answer: 61 . 3001 m (tolerance ± 1 %). Explanation: 44 m 18 m d 19 Note: ±igure is not drawn to scale. Basic Concepts: Δ x = d (cos θ ) Δ y = d (sin θ ) Δ x total = Δ x 1 + Δ x 2 Δ y total = Δ y 1 + Δ y 2 d total = r x total ) 2 + (Δ y total ) 2 Given: d 1 = 44 m θ 1 = 0 d 2 = 18 m θ 2 = 19 Solution: Δ x 1 = d 1 (cos θ 1 ) = (44 m)(cos 0 ) = 44 m Δ y 1 = d 1 (sin θ 1 ) = (44 m)(sin0 ) = 0 m Δ x 2 = d 2 (cos θ 2 ) = (18 m)[cos( 19 )] = 17 . 0193 m
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homework 04 – KERR, KELSEY – Due: Jan 28 2008, 11:00 pm 2 Δ y 2 = d 2 (sin θ 2 ) = (18 m)[sin( 19 )] = 5 . 86023 m Δ x total = Δ x 1 + Δ x 2 = 44 m + 17 . 0193 m = 61 . 0193 m Δ y total = Δ y 1 + Δ y 2 = 0 m + ( 5 . 86023 m) = 5 . 86023 m d total = r x total ) 2 + (Δ y total ) 2 = r (61 . 0193 m) 2 + ( 5 . 86023 m) 2 = 61 . 3001 m Question 4, chap 3, sect 1. part 2 of 2
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This note was uploaded on 04/18/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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4 - homework 04 KERR, KELSEY Due: Jan 28 2008, 11:00 pm...

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