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Please read ALL answers. NO CREDIT WILL BE GIVEN IF REASONING AND WORK IS NOT SHOWN. 1. The following conversion equivalents are given: mile = 5280 ft 1 ft = 12 in 1 m = 39.37 in 1 hour = 60 min 1 min = 60 s A car has a velocity of 6.5 miles per hour. The velocity, in meters/second, is closest to: (a) 3.5 m/s (b) 1.3 m/s (c) 31.3 m/s (d) 14.5 m/s (e) 2.9 m/s 2. You are given two vectors A = +5.0 i ˆ 2.0 ˆ j 2.0k ˆ and The scalar product of the two vectors is closest to: (a) 0.0 (b) 8.0 (c) -20.0 (d) 42.0 (e) -28.0 B = 2.0 i ˆ 7.0 ˆ j + 2.0 k ˆ 3. The components of vectors B and C are given as follows: B x = -7.3 C x = -7.8 B y = -8.6 C y = +9.8 The angle (less than 180 degrees) between vectors B and C, in degrees, is closest to: (a) 96 (b) 2 (c) 79 (d) 101 (e) 178
4. An airplane undergoes the following displacements: First, it flies 66 km in a direction 30 degrees east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30 degrees north of west. Using analytical methods, determine how far the airplane ends up from its starting point. (a) 79.1 km (b) 82.3 km (c) 75.9 km (d) 77.5 km (e) 80.7 km 5. A train moves at a constant velocity of 31 m/s. The train then decelerates uniformly at 0.065 m/s 2, until it is brought to a halt. The distance traveled by the train during deceleration, in km, is closest to: (a) 6.0 (b) 7.4 (c) 6.7 (d) 6.3 (e) 7.0 6. A ball is projected upward at time t = 0.0 s, from a point on a roof 80 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 56.7 m/s. Consider all quantities as positive in the upward direction. At time t = 2.9 s, the acceleration of the ball is closest to: (a) 0.0 (b) -4.9 m/s 2 (c) -9.8 m/s 2 (d) +4.9 m/s 2 (e) +9.8 m/s 2
7. A ball is projected upward at time t = 0.0 s, from a point on a roof 70 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 31.9 m/s. Consider all quantities as positive in the upward direction. The time when the ball strikes the ground is closest to: (a) 8.2 s (b) 8.5 s (c) 7.7 s (d) 8.8 s (e) 3.3 s 8. On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand 8.00 s later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 16.0 s. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is closest to: (a) 0.71 g (b) 2.00 g (c) 0.50 g (d) 0.25 g (e) 1.41 g 9. Which of the following situations is impossible? (a) An object has velocity directed east and acceleration directed west. (b) An object has velocity directed east and acceleration directed east. (c) An object has constant nonzero velocity and changing acceleration. (d) An object has zero velocity but nonzero acceleration. (e) An object has constant nonzero acceleration and changing velocity.
10. The figure shows the graph of the position x as a function of time for an object moving in the straight line (the x-axis). Which of the following graphs best describes the x-component of the velocity as a function of time for this object? (a) (b) (c) (d) (e) 11. The x- and y-coordinates of a particle in motion, as functions of time t, are given by: x = 7t 2-7t + 6 y = 4t 3-3t 2-12t - 5 At the instant the x-component of velocity is equal to zero, the y-component of the acceleration is closest to: (a) -18 m/s 2 (b) 6.0 m/s 2 (c) -30 m/s 2 (d) 0.00 m/s 2 (e) 18 m/s 2 12. A projectile is fired from the origin (at y = 0 m) as shown in the figure. The initial velocity components are v 0x = 270 m/s and v 0y = 80 m/s. The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. In Fig. 3.2, the y-component of the velocity of the shell of point P is closest to: (a) zero (b) +80 m/s (c) -80 m/s (d) -160 m/s (e) +160 m/s
13. Shown in the figure below are the trajectories of four artillery shells. Each was fired with the same speed. Which was in the air the longest time? (a) (b) (c) (d) (e) all are in the air the same time 14. An object moves in a circle of radius R at constant speed with a period t. If you want to change only the period in order to cut the object's acceleration in half, the new period should be: (a) t/4 (b) 1.41 t (c) t/1.41 (d) 4 t (e) 2 t 15. A hiker throws a stone from the upper edge of a vertical cliff. The stone s initial velocity is 25.0 m/s directed at 40.0 o with the face of the cliff, as shown in the figure below. The stone hits the ground 3.75 s after being thrown and feels no appreciable air resistance as it falls. The height of the cliff is closest to: (a) 141 m (b) 71.8 m (c) 60.3 m (d) 163 m (e) 129 m
Vectors Formula sheet A = A = A x 2 + A y 2 + A z 2 A = A xˆ i + A y ˆ j + A ˆ z k A B = ABcosθ A B = A x B y + A y B y + A z B z A B = ABsinθ A B The following always apply v x = dx a x = d v x v x average = x(t 2 ) x(t 1 ) t 2 t 1 a x average = v(t 2 ) v(t 1 ) t 2 t 1 The following apply for constant acceleration x x 0 = v x 0 t + 1 2 a x t 2 v x = v x 0 + a x t v 2 2 x = v x 0 + 2a x (x x 0 ) Other equations v = d r a = d v a c = v2 R = 4π 2 R T 2 v P / A = v P / B + v B / A Some constants g = 9.80 m s 2 1 km hr = 0.278 m s Some mathematical formulas: at 2 + bt + x = 0 t = b + if x(t) = at n dx = nat n 1 b2 4ac 2a