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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 xcomponent 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 ycomponent 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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 Spring '08
 Turner
 Acceleration, Work, Velocity, Correct Answer, vy

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