Homework 3 Solutions

Homework 3 Solutions - homework 03 – ALIBHAI ZAHID –...

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Unformatted text preview: homework 03 – ALIBHAI, ZAHID – Due: Feb 7 2007, 4:00 am 1 Question 1 part 1 of 1 10 points A ball rolling up a hill has vector velocities vectorv 1 and vectorv 2 at times t 1 and t 2 , respectively, as shown in the figure. v 1 initial v 2 final Which vector diagram below most accu- rately depicts the direction of the ball’s aver- age acceleration over the interval? 1. 2. 3. 4. 5. 6. correct 7. 8. 9. Zero vector. Explanation: In fact the two forces exerting on the ball, the gravitational force from the earth and the force from the incline remain unchanged dur- ing the interval, to total acceleration should be downward to the left and won’t change either. Question 2 part 1 of 2 10 points A truck driver attempting to deliver some furniture travels 6 km east, turns around and travels 2 km west, and then travels 11 km east to his destination. a) What distance has the driver traveled? Correct answer: 19 km (tolerance ± 1 %). Explanation: Basic Concept: d = | Δ x 1 | + | Δ x 2 | + | Δ x 3 | Let: Let North and East be positive Δ x 1 = 6 km , Δ x 2 = − 2 km , Δ x 3 = 11 km , and Δ y = 0 km . Solution: d = (6 km) + (2 km) + (11 km) = 19 km . Question 3 part 2 of 2 10 points homework 03 – ALIBHAI, ZAHID – Due: Feb 7 2007, 4:00 am 2 b) What is the magnitude of the driver’s total displacement? Correct answer: 15 km (tolerance ± 1 %). Explanation: Basic Concept: d 1 = Δ x 1 + Δ x 2 + Δ x 3 Solution: Displacement is a vector d 1 = (6 km) − (2 km) + (11 km) = 15 km . Question 4 part 1 of 2 10 points A commuter airplane starts from an airport and takes the route shown in the figure. It first flies to city A located at 191 km in a direction 28 ◦ north of east. Next, it flies 154 km 17 ◦ west of north to city B . Finally, it flies 155 km due west to city C . 1 9 1 k m 28 ◦ A 1 5 4 k m 17 ◦ B 155 km C R C x (km) y (km) 50 100 150 200 50 100 150 200 250 W E S N How far away from the starting point is city C ? Correct answer: 239 . 009 km (tolerance ± 1 %). Explanation: Given : a = 191 km , α = 28 ◦ , b = 154 km , β = 17 ◦ , and c = 155 km . a b α β The x-component of the resultant is r x = a x + b x + c x = a cos α − b sin β − c = (191 km) cos28 ◦ − (154 km) sin17 ◦ − 155 km = − 31 . 3823 km . The y-component of the resultant is r y = a y + b y + c y = a sin α + b cos β + 0 = (191 km) sin28 ◦ + (154 km) cos 17 ◦ = 236 . 94 km . and the resultant is R = radicalBig r x 2 + r y 2 = radicalBig ( − 31 . 3823 km) 2 + (236 . 94 km) 2 = 239 . 009 km . Question 5 part 2 of 2 10 points What is the direction of the final position vector r , measured from North? Use coun- terclockwise as the positive angular direction, between the limits of − 180 ◦ and +180 ◦ ....
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Homework 3 Solutions - homework 03 – ALIBHAI ZAHID –...

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