Practice Test 1 1. A steel cylinder is 39 mm in height and 39 mm in diameter.

Transcription

1 Practice Test 1 1. A steel cylinder is 39 mm in height and 39 mm in diameter. (a) How much does it weigh? (density of steel: ρ = 7560 kg/m3) 2. An automobile moving along a straight track changes its velocity from 40 m/s to 80 m/s in a distance of 200 m. What is the (constant) acceleration of the vehicle during this time? a. 8.0 m/s b. 9.6 m/s c. 12 m/s d. 6.9 m/s e m/s 3. An automobile traveling along a straight road increases its speed from 30.0 m/s to 50.0 m/s in a distance of 180 m. If the acceleration is constant, how much time elapses while the auto moves this distance? a s b s c s d s e s 4. A particle starts from rest at x = 0 m and v = 0 m/s and moves for 10 s with an acceleration of +2.0 cm/s 2. For the next 20 s, the acceleration of the particle is 1.0 cm/s 2. Draw a graph of acceleration vs. time Draw a graph of velocity vs. time Draw a graph of position vs. time What is the position of the particle at the end of this motion? a. zero b m c. 1.0 m d m e. 3.0 m 5. A toy rocket, launched from the ground, rises vertically with an acceleration of 20 m/s 2 for 6.0 s until its motor stops. Disregarding any air resistance, what maximum height above the ground will the rocket achieve? a. 1.1 km b km c. 1.9 km d km e. 1.5 km

2 6. A speedy tortoise can run with a velocity of 0.1 m/s and a hare can run 2.0 m/s. In a race, the hare gives the tortoise a 2-minutes head start. The tortoise wins the race by a shell (0.2 m). What was the length of the race? 7. A melon truck brakes right before a ravine and loses a few melons. The melons skit over the edge with an initial velocity of v x = 10.0 m/s. a. Determine the x- and y-components of the velocity of a melon at any time and the total velocity at any time. b. Calculate the velocity and the speed of the melon at t = 5.00 s. c. Determine the x- and y-coordinates of the particle at any time t and the position vector r at any time t. d. Graph the path of a melon. 8. If A = 12i 16j and B = 24i + 10j, what is the magnitude of the vector C = 2A B? a. 42 b. 22 c. 64 d. 90 e If A = 12i 16j and B = 24i + 10j, what is the direction of the vector C = 2A B? a. 49 b. 41 c. 90 d. +49 e A particle starts from the origin at t = 0 with a velocity of 8.0j m/s and moves in the x-y plane with a constant acceleration of (4.0i + 2.0j) m/s 2. At the instant the x coordinate of the particle is 29 m, what is the value of its y coordinate?

3 a. 35 m b. 39 m c. 45 m d. 42 m e. 29 m 11. 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/s 2. 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 12. A particle moves in the xy plane with a constant acceleration given by a = 4.0j m/s 2. At t = 0 its position and velocity are 10i m and ( 2.0i 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 13. 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/s 2. 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 14. 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

4 15. 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 16. 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. Problem 1: A baseball is thrown. For the each of the indicated positions of the baseball along its trajectory, draw and label the following vectors: the x-component of the velocity, the y-component of the velocity, and the acceleration. Explain why you drew the vectors as you did. Problem 2: A rock is thrown with an initial vertical velocity component of 30 m/s and an initial horizontal velocity component of 40 m/s. a. What will these velocity components be one second after the rock reaches the top of its path? b. Assuming the launch and landing heights are the same, how long will the rock be in the air? c. Assuming the launch and landing heights are the same, how far will the rock land from where it was thrown?

5 Problem 3: Two tennis ball launchers shoot balls at the same time, angle and initial speed from different floors of a tall building. The balls land in the street below. Ignore air resistance. a. Which ball will have the greater acceleration while in flight? Explain your reasoning. b. Which ball will hit farther from the base of the building? Explain your reasoning. c. Which ball will reach a greater maximum height? Explain your reasoning. d. Which ball will be going faster just before hitting the street? Explain your reasoning. e. How could you adjust only the angle of the upper launcher so that the ball hits in the same place as the ball from the lower launcher? Explain your reasoning. f. How could you adjust only the angle of the lower launcher so that the ball hits in the same place as the ball from the upper launcher? Explain your reasoning. Problem 4: Balls A and B are launched from different heights. They reach the same maximum height at exactly the same point in space. a. Which ball has a greater initial vertical component of velocity? Explain. b. Which ball has a greater initial horizontal component of velocity? Explain. c. Which ball has the larger launch angle? Explain. d. Which ball has greater acceleration while in flight? Explain. e. Which ball will land farther from the launchers? Explain. f. Which ball takes longer to reach maximum height? Explain. g. If the balls were launched simultaneously, would they collide before landing? Explain.

6 Problem 5: If a person can jump a horizontal distance of 3 m on Earth, how far could the person jump on the moon where the acceleration due to gravity is one-sixth of that on earth (1.7 m/s 2 )? Problem 6: A brick is thrown upward from the top of a building at an angle of 25 degrees above the horizontal and with an initial speed of 15 m/s. If the brick is in the air for 3 seconds, how high is the building? (Draw a picture.) Problem 7: A daredevil tries to jump a canyon of width 10 m. To do so, he drives his motorcycle up an incline sloped at an angle of 15 degrees. What minimum speed is necessary to clear the canyon? Problem 8: A woman stands on a scale in a moving elevator. Her mass is 50.0 kg, and the combined mass of the elevator and scale is an additional 815 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9530 N. What does the scale read during the acceleration? Problem 9: An object of mass m 1 = 45 kg sits on a horizontal frictionless table. A rope is attached to it, which runs horizontally to a frictionless pulley, then down to a hanging mass m 2 = 5 kg a. Find the acceleration of each mass, b. what is the size of the tension in the rope? Problem 10: A boat heading due north crosses a river with a speed of 10.0 km/h. The water in the river has a speed of 5.0 km/h due east. a. Determine the velocity of the boat. b. If the river is 3.0 km wide how long does it take to cross it?