Exam 1 Practice Problems 1. (hr02-041) As two trains move along a track, their conductors suddenly notice that they are headed toward each other. The figure to the right gives their velocities v as functions of time t as the conductors slow the trains. The figure’s vertical scaling is set by vs = 40.0 m/s. The slowing processes begin when the trains are 200 m apart. What is their separation when both trains have stopped? Answer: 40 m. 2. (hr02-075) To stop a car, first you require a certain reaction time to begin braking; then the car slows at a constant rate. Suppose that the total distance moved by your car during these two phases is 56.7 m when its initial speed is 80.5 km/h, and 24.4 m when its initial speed is 48.3 km/h. What are (a) your reaction time and (b) the magnitude of the acceleration? Answer: (a) 0.74 s (b) 6.2m/s2. 3. (hr02-059) Water drips from the nozzle of a shower onto the floor 200cm below. The drops fall at regular (equal) intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall. When the first drop strikes the floor, how far below the nozzle are the (a) second and (b) third drops? Answer: (a) 89 cm, (b) 22 cm. 4. (hr04-015) A particle leaves the origin with an initial velocity ⃗ = (3.00m/s)̂ and a constant acceleration ⃗ = (−1.00m/s2 )̂ + (−0.500m/s 2 )̂. When it reaches its maximum x coordinate, what are its (a) velocity and (b) position vector? Answer: (a)(−1.50m/s)̂, (b) (4.50m)̂ + (−2.25m)̂ 5. (hr04-086) A radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d1 = 360 m from the station and at angle θ1 = 40° above the horizon (See figure). The airplane is tracked through an angular change ∆θ = 123° in the vertical east–west plane; its distance is then d2 = 790 m. Find the (a) magnitude and (b) direction of the airplane’s displacement during this period. Answer: (a) 1.03 km, (b) almost exactly horizontally westward (0.02 degrees below westward) 6. (hr04-039) In the figure to the right, a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.50 s later, at distance d = 25.0 m from the building and at angle θ = 60.0° with the horizontal. (a) Find h. (Hint: One way is to reverse the motion, as if on video.) What are the (b) magnitude and (c) angle, relative to the horizontal, of the velocity at which the ball is thrown? (d) Is the angle above or below the horizontal? Answer: (a) 32.3 m, (b) 21.9 m/s, (c) 40.4°, (d) below. 7. (hr04-075) A train travels due south at 30 m/s (relative to the ground) in a rain that is blown toward the south by the wind. The path of each raindrop makes an angle of 70° with the vertical, as measured by an observer stationary on the ground. An observer on the train, however, sees the drops fall perfectly vertically. Determine the speed of the raindrops relative to the ground. Answer: 32 m/s. 8. (hr04-081) Ship A is located 4.0 km north and 2.5 km east of ship B. Ship A has a velocity of 22 km/h toward the south, and ship B has a velocity of 40 km/h in a direction 37° north of east. (a) What is the velocity of A relative to B in unit-vector notation with toward the east? (b) Write an expression (in terms of ̂ and ̂) for the position of A relative to B as a function of t, where t=0 occurs when the ships are in the positions described above. (c) At what time is the separation between the ships least? (d) What is that least separation? Answer: (a) (−32 km/h)̂ + (−46 km/h)̂, (b) [(2.5 km) + (−32 km/h)t]̂ + [(4.0 km) + (−46 km/h)t]̂, (c) 0.084 h, (d) 0.20 km 9. (hr04-059) A woman rides a carnival Ferris wheel (the wheel is vertical with a horizontal axis of rotation) at radius 15 m, completing five turns about its horizontal axis every minute. What are (a) the period of the motion, the (b) magnitude and (c) direction of her centripetal acceleration at the highest point, and the (d) magnitude and (e) direction of her centripetal acceleration at the lowest point? Answer: (a) 12 s, (b) 4.1 m/s2, (c) down, (d) 4.1 m/s2, (e) up 10. (hr05-043) In Fig. 5-43, a chain consisting of five links, each of mass 0.100 kg, is lifted vertically with constant acceleration of magnitude a = 2.50 m/s2. Find the magnitudes of (a) the force on link 1 from link 2, (b) the force on link 2 from link 3, (c) the force on link 3 from link 4, and (d) the force on link 4 from link 5. Then find the magnitudes of (e) the force ⃗ on the top link from the person lifting the chain and (f) the net force accelerating each link. Answer: (a) 1.23 N, (b) 2.46 N, (c) 3.69 N, (d) 4.92 N, (e) 6.15 N, (f) 0.250 N 11. (hr05-055) Two blocks are in contact on a frictionless table. A horizontal force is applied to the larger block, as shown in the figure. (a) If m1 = 2.3 kg, m2 = 1.2 kg, and F = 3.2 N, find the magnitude of the force between the two blocks. (b) A force of the same magnitude F is applied to the smaller block but in the opposite direction, find now the magnitude of the force between the blocks, which is NOT the same value calculated in (a). (c) Why are the two values different? Answer (a) 1.1 N, (b) 2.1 N 12. (hr05-061) A hot-air balloon of mass M is descending vertically with downward acceleration of magnitude a. How much mass (ballast) must be thrown out to give the balloon an upward acceleration of magnitude a? Assume that the upward force from the air (the lift) does not change because of the decrease in mass. Answer: 2/( + )

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