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#### Multiple Choice 1

###### Physics

Multiple Choice

1.   A particle starts from the origin at t = 0 with a velocity of 8.0j  m/s and moves in the xy  plane with a constant acceleration of (4.0i + 2.0j) m/s2.  At the instant the x coordinate of the particle is 29 m, what is the value of its y coordinate?

a. 35 m              b. 39 m          c. 45 m          d. 42 m          e. 29 m

2.   At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i – 4.0j) m/s2.  At the instant the x coordinate of the particle is 15 m, what is the speed of the particle?

a. 10 m/s           b. 16 m/s       c. 12 m/s        d. 14 m/s       e. 26 m/s

3.   A particle starts from the origin at t = 0 with a velocity of 6.0i m/s and moves in the xy plane with a constant acceleration of (–2.0i + 4.0j) m/s2.  At the instant the particle achieves its maximum positive x coordinate, how far is it from the origin?

a. 36 m              b. 20 m          c. 45 m          d. 27 m          e. 37 m

4.   A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0i – 2.0j) m/s2.  At the instant the particle moves back across the x axis (y = 0), what is the value of its x coordinate?

a. 65 m              b. 91 m          c. 54 m          d. 78 m          e. 86 m

5.   At t = 0 a particle leaves the origin with a velocity of 5.0 m/s in the positive y direction.  Its acceleration is given by a = (3.0i – 2.0j) m/s2.  At the instant the particle reaches its maximum  y coordinate how far is the particle from the origin?

a. 11 m              b.  16 m         c. 22 m          d. 29 m          e. 19 m

6.   A particle moves in the xy plane with a constant acceleration given by a = –4.0j  m/s2.  At t = 0 its position and velocity are 10i m and (–2.0i  + 8.0 j) m/s, respectively.  What is the distance from the origin to the particle at t = 2.0 s?

a. 6.4 m             b. 10 m          c. 8.9 m         d. 2.0 m         e. 6.2 m

7.   A particle starts from the origin at t = 0 with a velocity of (16i – 12j) m/s and moves in the xy plane with a constant acceleration of a = (3.0i – 6.0j) m/s2.  What is the speed of the particle at t = 2.0 s?

a. 52 m/s           b. 39 m/s       c. 46 m/s        d. 33 m/s       e. 43 m/s

8.   At t = 0, a particle leaves the origin with a velocity of 12 m/s in the positive x direction and moves in the xy plane with a constant acceleration of (–2.0i + 4.0j) m/s2.  At the instant the y coordinate of the particle is 18 m, what is the x coordinate of the particle?

a. 30 m              b. 21 m          c. 27 m          d. 24 m          e. 45 m

9.   At t = 0, a particle leaves the origin with a velocity of 12 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i – 4.0j) m/s2.  At the instant the particle moves back across the x axis (y = 0), what is the speed of the particle?

a. 16 m/s           b. 17 m/s       c. 18 m/s        d. 14 m/s       e. 22 m/s

10. The initial speed of a cannon ball is 0.20 km/s.  If the ball is to strike a target that is at a horizontal distance of 3.0 km from the cannon, what is the minimum time of flight for the ball?

a. 16 s               b. 21 s           c. 24 s            d. 14 s           e. 19 s

11. A ball is thrown horizontally from the top of a building 0.10 km high.  The ball strikes the ground at a point 65 m horizontally away from and below the point of release.  What is the speed of the ball just before it strikes the ground?

a. 43 m/s           b. 47 m/s       c. 39 m/s        d. 36 m/s       e. 14 m/s

12. A baseball is hit at ground level.  The ball is observed to reach its maximum height above ground level 3.0 s after being hit.  And 2.5 s after reaching this maximum height, the ball is observed to barely clear a fence that is 97.5 m from where it was hit.  How high is the fence?

a. 8.2 m             b. 15.8 m       c. 13.4 m       d. 11.0 m       e. 4.9 m

13. A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal.  The rock strikes the ground a horizontal distance of 25 m from the base of the building.  Assume that the ground is level and that the side of the building is vertical.  How tall is the building?

a. 25.3 m           b. 29.6 m       c. 27.4 m       d. 23.5 m       e. 18.9 m

14. A rock is projected from ground level.  Later, 4.0 s after being projected, the rock is observed to strike the top of a 9.75 m tall fence that is a horizontal distance of 240 ft from the point of projection.  Determine the speed with which the rock was projected.

a. 27.7 m/s        b. 29.6 m/s    c. 28.7 m/s     d. 26.8 m/s    e. 25.8 m/s

15. A projectile is thrown from the top of a building with an initial velocity of 30 m/s in the horizontal direction.  If the top of the building is 30 m above the ground, how fast will the projectile be moving just before it strikes the ground?

a. 35 m/s           b. 39 m/s       c. 31 m/s        d. 43 m/s       e. 54 m/s

16. The initial speed of a projectile is 80 m/s.  If the projectile is to strike a target that is a horizontal distance of 0.45 km away, what is the minimum time of flight?

a. 9.0 s              b. 6.9 s          c. 7.8 s           d. 6.1 s          e. 5.6 s

17. A rifle is aimed horizontally at the center of a large target 60 m away.  The initial speed of the bullet is 240 m/s.  What is the distance from the center of the target to the point where the bullet strikes the target?

a. 48 cm            b. 17 cm        c. 31 cm         d. 69 cm        e. 52 cm

18. A rock is projected from the edge of the top of a 100-ft tall building at some unknown angle above the horizontal.  The rock strikes the ground a horizontal distance of 160 ft from the base of the building 5.0 s after being projected.  Assume that the ground is level and that the side of the building is vertical.  Determine the speed with which the rock was projected.

a. 72 ft/s            b. 77 ft/s        c. 68 ft/s        d. 82 ft/s        e. 87 ft/s

19. An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m.  Assume that the ground is level.  What horizontal distance from a target must the pilot release a bomb so as to hit the target?

a. 3.0 km           b. 2.4 km       c. 3.3 km       d. 2.7 km       e. 1.7 km

20. An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m.  What is the magnitude of the instantaneous acceleration of the particle during this time?

a. 2.2 m/s2        b. 2.7 m/s2    c. 3.3 m/s2     d. 3.8 m/s2    e. 2.9 m/s2

21. A particle moves at a constant speed in a circular path with a radius of 2.0 cm.  If the particle makes four revolutions each second, what is the magnitude of its acceleration?

a. 20 m/s2         b. 18 m/s2     c. 13 m/s2      d. 15 m/s2     e. 24 m/s2

22. A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s.  What is the magnitude of the acceleration of the race car?

a. 8.8 m/s2        b. 7.5 m/s2    c. 9.4 m/s2     d. 6.3 m/s2    e. 5.3 m/s2

23. At the lowest point in a vertical dive (radius = 0.60 km), an airplane has a speed of 300 km/h which is not changing.  Determine the magnitude of the acceleration of the pilot at this lowest point.

a. 26 m/s2         b. 21 m/s2     c. 16 m/s2      d. 12 m/s2     e. 8.8 m/s2

24. A carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute.  What is the acceleration of a passenger at his lowest point during the ride?

a. 5.7 m/s2 downward                                  b. 4.1 m/s2 upward

c. 14 m/s2 downward                                   d. 4.1 m/s2 downward

e. 19 m/s2 downward

25. A space station of diameter 80 m is turning about its axis at a constant rate.  If the acceleration of the outer rim of the station is 2.5 m/s2, what is the period of revolution of the space station?

a. 22 s               b. 19 s           c. 25 s            d. 28 s           e. 40 s

26. A car travels counterclockwise around a flat circle of radius 0.25 km at a constant speed of 20 m/s.  When the car is at point A as shown in the figure, what is the car's acceleration?

 a. 1.6 m/s2, east b. Zero c. 1.6 m/s2, east d. 1.6 m/s2, north e. 1.6 m/s2, west

27. A particle moves along a circular path having a radius of 2.0 m.  At an instant when the speed of the particle is equal to 3.0 m/s and changing at the rate of 5.0 m/s2, what is the magnitude of the total acceleration of the particle?

a. 7.5 m/s2         b. 6.0 m/s2     c. 5.4 m/s2     d. 6.7 m/s2     e. 4.5 m/s2

28. A car travels in a flat circle of radius R.  At a certain instant the velocity of the car is 20 m/s north, and the total acceleration of the car is 2.5 m/s2 37° south of west.  Which of the following is correct?

a. R = 0.40 km, and the car's speed is decreasing.

b. R = 0.20 km, and the car's speed is decreasing.

c. R = 0.20 km, and the car's speed is increasing.

d. R = 0.16 km, and the car's speed is increasing.

e. R = 0.16 km, and the car's speed is decreasing.

29. A car travels in a flat circle of radius R.  At a certain instant the velocity of the car is 24 m/s west, and the total acceleration of the car is 2.5 m/s2 53° north of west.  Which of the following is correct?

a. R = 0.29 km, and the car's speed is increasing.

b. R = 0.23 km, and the car's speed is decreasing.

c. R = 0.23 km, and the car's speed is increasing.

d. R = 0.29 km, and the car's speed is decreasing

e. R = 0.29 km, and the car's speed is constant.

30. A stunt pilot performs a circular dive of radius 800 m.  At the bottom of the dive (point B in the figure) the pilot has a speed of 200 m/s which at that instant is increasing at a rate of 20 m/s2.  What acceleration does the pilot have at point B?

 a. (50i + 20j) m/s22 b. (20i – 50j) m/s2 c. (20i + 50j) m/s2 d. (–20i + 50j) m/s2 e. (–50i + 20j) m/s2

31. The speed of a particle moving in a circle 2.0 m in radius increases at the constant rate of 4.4 m/s2.  At an instant when the magnitude of the total acceleration is 6.0 m/s2, what is the speed of the particle?

a. 3.9 m/s          b. 2.9 m/s      c. 3.5 m/s       d. 3.0 m/s      e. 1.4 m/s

32. A car travels in a flat circle of radius R.  At a certain instant the velocity of the car is 24 m/s, west and the acceleration of the car has components of 2.4 m/s2 east and 1.8 m/s2 south.  What is the radius of the circle?

a. 0.24 km         b. 0.19 km     c. 0.32 km     d. 0.14 km     e. 0.27 km

33. A particle moves in the xy plane in a circle centered on the origin.  At a certain instant the velocity and acceleration of the particle are 6.0i m/s and (3.0i + 4.0j) m/s2.  What are the x and y coordinates of the particle at this moment?

a. x = 0, y = –9.0 m                 b. x = 0, y = +7.2 m

c. x = 0, y = +9.0 m                d. x = 0, y = –7.2 m

e. x = 6.0, y = –9.0 m

34. A particle moves in the xy plane in a circle centered on the origin.  At a certain instant the velocity and acceleration of the particle are 4.0j m/s, and (–3.0i – 2.0j) m/s2.  What are the x and y coordinates of the particle at this moment?

a. x = –4.4 m, y = 0                 b. x = +5.3 m, y = 0

c. x = –5.3 m, y = 0                 d. x = +4.4 m, y = 0

e. x = –1.8 m, y = 0

35. A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east.  It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank.  What is the speed of the boat relative to the water?

a. 5.7 m/s          b. 8.5 m/s      c. 8.1 m/s       d. 7.0 m/s      e. 6.4 m/s

36. A 0.20-km wide river has a uniform flow speed of 4.0 m/s toward the east.  It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank.  In what direction must the boat be pointed so as to accomplish this?

a. 23° west of north                b. 21° west of north

c. 24° west of north                d. 22° west of north

e. 17° west of north

37. A 0.20-km wide river has a uniform flow speed of 3.0 m/s toward the east.  A boat with a speed of 8.0 m/s relative to the water leaves the south bank and heads in such a way that it crosses to a point directly north of its departure point.  How long does it take the boat to cross the river?

a. 29 s               b. 23 s           c. 25 s            d. 27 s           e. 17 s

38. A river has a steady speed of 0.30 m/s.  A student swims downstream a distance of 1.2 km and returns to the starting point.  If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes, how much time is required for the entire swim?

a. 50 minutes                    b. 80 minutes                  c. 90 minutes

d. 70 minutes                    e. 60 minutes

39. The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east.  If his speed relative to the ground is 80 km/h, what is the speed of his airplane relative to the air?

a. 89 km/h         b. 85 km/h     c. 81 km/h     d. 76 km/h     e. 72 km/h

40. A car travels in a due northerly direction at a speed of 55 km/h.  The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal.  If the rain is falling vertically with respect to the earth, what is the speed of the rain with respect to the earth?

a. 48 km/h         b. 95 km/h     c. 58 km/h     d. 32 km/h     e. 80 km/h

Conceptual Problems

41. Wiley Coyote has missed the elusive roadrunner once again.  This time, he leaves the edge of the cliff at 50 m/s horizontal velocity.  If the canyon is 100 m deep,  how far from the edge of the cliff does the coyote land?

42. A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20° above the horizontal.  How long is he in the air before returning to Earth?

43. An artillery shell is fired with an initial velocity of 300 m/s at 55° above the horizontal.  It explodes on a mountainside 42 s after firing.  If x is horizontal and y vertical, find the (x, y) coordinates where the shell explodes.

44. In a TV set, an electron beam moves horizontally at 3.0 x 107 m/s across the cathode ray tube and strikes the screen, 42 cm away.  How far does the electron beam fall while traversing this distance?

45. A football is thrown upward at a 30° angle to the horizontal.  To throw a 40.0-m pass, what must be the initial speed of the ball?

46. A satellite is in a circular orbit 600 km above the Earth's surface.  The acceleration of gravity is 8.21 m/s2 at this altitude.  The radius of the Earth is 6400 km.  Determine the speed of the satellite, and the time to complete one orbit around the Earth.

47. A tennis player standing 12.6 m from the net hits the ball at 3.0° above the horizontal.  To clear the net, the ball must rise at least 0.33 m.  If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

48. A rifle is aimed horizontally toward the center of a target 0.10 km away, but the bullet strikes 10 cm below the center.  Calculate the velocity of the bullet just as it emerges from the rifle.

Multiple Choice Conceptual Problems

49. Two cars are traveling around identical circular racetracks.  Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that:

a. it is passing car A.

b. it has the same linear (tangential) acceleration as car A.

c. it has the same centripetal acceleration as car A.

d. it has the same total acceleration as car A.

e. it has traveled farther than car A since starting.

50. A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity. The speed of the ball as seen by a stationary observer in the street:

a. is less than that observed inside the bus.

b. is the same as that observed inside the bus.

c. is greater than that observed inside the bus.

d. may be either greater or smaller than that observed inside the bus.

e. cannot be determined without knowing the magnitudes of the velocities.

51. Two balls, projected at different times so they don't collide, have trajectories A and B, as shown below.

Which statement is correct?

a. voB must be greater than voA.

b. Ball A is in the air for a longer time than ball B.

c. Ball B is in the air for a longer time than ball A.

d. Ball B has a greater acceleration than ball A.

e. Ball A has a greater acceleration than ball B.

52. The vector r indicates the instantaneous displacement of a projectile from the origin. v is the instantaneous velocity of the projectile and a its acceleration when at r. Which statement is correct?

a. v is always perpendicular to  r.

b. a is always perpendicular to r.

c. a is always perpendicular to v.

d. a is always perpendicular to vx.

e. a is always perpendicular to vy.

53. A projectile starts at the coordinate origin, where the displacement vector also originates.  The initial velocity, v0, makes an angle θ0 with the horizontal where 0 < θ < 90°.  At the instant when the projectile is at the highest point of its trajectory, the displacement, velocity and acceleration vectors are r, v and a. Which statement is true?

a. r is parallel to v.

b. r is perpendicular to v.

c. v is parallel to a.

d. v is perpendicular to a.

e. r is perpendicular to a.

Conceptual and Calculation

54. A car travels in an oval path as shown below. vA = 25 m/s, West, and vB = 20 m/s, North. The ratio of the magnitude of the acceleration at B to that at A, ab/aa is:

 a. 0.512 b. 0.64 c. 0.8 d. 1.25 e. 1.56

55. Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater.  Each glob lands on the top of a tin the same horizontal distance away and at its initial height.  However, one lands later than the other. The explanation is that they left the beaters at angles θ1 and θ2 such that:

a. θ2 = –θ1.                      b. θ1 + θ2 = π/4            c. θ1 + θ2 = π/2

d. θ1 + θ2 = π.                 e. θ1 – θ2 = π.

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