phys1hw3 - homework 03 – ANDERSON ZACH – Due 4:00 am 1...

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Unformatted text preview: homework 03 – ANDERSON, ZACH – Due: Sep 15 2007, 4:00 am 1 Question 1, chap 4, sect 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. Zero vector. 6. correct 7. 8. 9. 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, chap 4, sect 3. 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 35 ◦ north of east. Next, it flies 137 km 24 ◦ west of north to city B . Finally, it flies 180 km due west to city C . 1 9 1 k m 35 ◦ A 1 3 7 k m 24 ◦ B 180 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: 247 . 732 km (tolerance ± 1 %). homework 03 – ANDERSON, ZACH – Due: Sep 15 2007, 4:00 am 2 Explanation: Given : a = 191 km , α = 35 ◦ , b = 137 km , β = 24 ◦ , and c = 180 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) cos 35 ◦- (137 km) sin24 ◦- 180 km =- 79 . 2649 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) sin35 ◦ + (137 km) cos24 ◦ = 234 . 709 km . and the resultant is R = radicalBig r x 2 + r y 2 = radicalBig (- 79 . 2649 km) 2 + (234 . 709 km) 2 = 247 . 732 km . Question 3, chap 4, sect 3. 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 ◦ . Correct answer: 18 . 6606 ◦ (tolerance ± 1 %). Explanation: r γ r y r x Since γ is the angle between r and the y- axis, for r is in the second quadrant tan γ = | r x | | r y | . Thus γ = tan − 1 parenleftbigg | r x | | r y | parenrightbigg = tan − 1 parenleftbigg 79 . 2649 km 234 . 709 km parenrightbigg = 18 . 6606 ◦ . Question 4, chap 4, sect 3. part 1 of 2 10 points A particle travels horizontally between two parallel walls separated by 18 . 4 m. It moves toward the opposing wall at a constant rate of 5 . 9 m / s. Also, it has an acceleration in the direction parallel to the walls of 2 m / s 2 . It hits the opposite wall at a higher point. 18 . 4 m 2m / s 2 5 . 9 m / s a) What will be its speed when it hits the opposing wall?...
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phys1hw3 - homework 03 – ANDERSON ZACH – Due 4:00 am 1...

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