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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 xcomponent 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 ycomponent 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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This note was uploaded on 04/10/2008 for the course PHY 303K taught by Professor Turner during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Turner
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