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physics 105 fall 2006 solutions 1A g 9.8 1. In May 1998, forest fires in southern Mexico and Guatemala spread smoke all the way to Austin. Those fires consumed forest land at a rate of 23100 v 23100 acres/week. How many square meters of forest are burned down every minute?. (1 acre = 4.84 103 yd2 acre 60.5 80 , 1 yd = 36 yd 36 inch, 1 inch = 2.54 cm. ) A) 4072 B) 5463 C) 6826 D) 8047 E) 9274 1E 2 2 v acre yd in 3 1. acre w l week 7 24 60 minutes v v 9.274 10 week 2. The information on a one-gallon paint can is that the coverage, when properly applied, is 450 ft2 One gallon is 231 in3 . What is the average thickness of the paint in such an application? A) 0.0036 in B) 0.043 in C) 0.090 in D) 0.21 in E) 0.51 in 2A gal 3 d a ft 12 d 3.565 10 2 A ft 2 3. A particle moves according to the equation x = 5 - 12.t + 3.t2 x( t ) 5 12 t 3 t where x is in meters and t is in seconds. Find the position of the particle at t = 2 seconds. A) 0 B) 3 C) 6 D) -12 E) -7 x( 2) 7 4. An automobile travels on a straight road for 40 km at 20 km/hr. It then continues in the same direction for another 40 km at 80 km/hr v2 80. What is the average velocity of the car during this 80 km trip? A) 32 B) 36 C) 42 D) 46 E) 50 L L time to make first 40 km distance t1 time to make the second 40 km distance t2 total distance = 2L v1 v2 2L total time = t1 + t2 vavg vavg 32 t1 t2 5. Add the two vectors shown. The magnitude of the result is: A) 10.9 B) 16.9 C) 28.7 D) 32.9 E) 36 5B 37 deg Sum 21 j ( 15 cos ( ) i 15 sin( ) j) Sum 16.937 A = 2i points east and vector B = -5j points south. If vector C = B – A , then vector C points: 6. Vector A) - 680 B) 680 A 2 i B C) -1120 D) +1120 E) none of these 2 5 j C B A C angle( C i) 111.801 5 7. A train slowly climbs a 500-m mountain track which is at an angle of 100 with respect to the horizontal. How much altitude does it gain? h L sin( ) A) 86.8 m B) 88.2 m C) 341 m D) 492 m E) 50.7 m 7A h 86.824 8. Find the resultant of the following two vectors: i) 50 units due east A 50 i and ii) 100 units 300 north of west B 150 deg . vector B = B 100 cos ( B) i 100 sin( B) j A) 100 units 300 north of west B) 62 units 150 north of west C) 87 units 600 north of west D) 62 units 540 north of west E) 126 units 150 north of east 8D C A B C 36.603 50 C 61.966 angle( C i) 126.206 9. A velocity vs time plot of a runner is shown in the figure. What is the distance he made between 2 and 6 seconds? distance = 2*0.6+2*0.3 10. A ball is rolled horizontally off a table with an initial speed of 0.24 m/s. A stopwatch measures the ball’s trajectory time from table to the floor to be 0.30 s. What is the height of the table? (g = 9.8 m/s 2 and air resistance is negligible) 1 2 A) 0.11 m B) 0.22 m C) 0.33 m D) 0.44 m E) 0.55 m 10D g t 0.441 2 11. A track star in the broad jump goes into the jump at 12 m/s vo 12 and launches himself at 200 above the horizontal 20 deg . How long is he in the air before returning to Earth? (g = 9.8 m/s 2) 2 vo sin( ) A) 0.42 s B) 0.84 s C) 1.25 s D) 1.48 s E) 1.68 11B 0.838 g 12. A ball is launched from ground level at 30 m/s vo 30 at an angle of 350 35 deg above the horizontal. How far does it go before it is at ground level again? A) 14 m B) 21 m C) 43 m D) 86 m E) 106 m 12D R 2 vo sin ( 2 ) R 86.298 g Workout problems: Workout problem 1 - 3 points Oasis B is 25 km due east of oasis A. Starting from oasis A, a camel walks 24 km in a direction 15 0 south of east 15 deg . How far is the camel then from oasis B? Oasis B location is at B 25 i 0 j first displacement vector from oasis A is A 24 cos ( ) i 24 sin( ) j The camels should walk first a vector A (known) then a vector x i y j (unknown) to finish at oasis B (location known) we can write that A ( x i y j) B so [24cos()+x]i + 24sin()+y]j = 25i + 0j equations for x and y components are respectively 24 cos ( ) x 25 and 24 sin( ) y 0 x 25 24 cos ( ) y 24 sin( ) Workout problem 2 - 2 points x 1.818 2. A jumbo jet must reach a speed of 400 km/hr v y 6.212 400 1000 and the distance is 2 x 2 y 6.472 m/s on the runway for takeoff. 3600 a) What is the least constant acceleration needed for takeoff from a 2 km x 2000 runway? b) How much time it would take to cover the distance of 2 km? a) v b) x 2 2 0 1 2 at 2 2 2 a x >> >> a t v 2x 2x a a 3.086 t 36