Survey

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Survey

Transcript

[Use the gravitational acceleration ππ as 9.8 m/s2 throughout the problems.] 1. At a stop light, a truck traveling at 16 m/s passes a car as it starts from rest. The truck travels at constant velocity and the car accelerates at 2 m/s2. How much time does the car take to catch up to the truck? (5 pt) 2. Two vectors lie with their tails at the same point. When the angle between them is increased by 30°, the magnitude of their vector product becomes β3 times larger. What was the original angle between them? (10 pt) 3. A ball is thrown horizontally from the top of a 500-m high hill. It strikes the ground at an angle of 45°. With what speed was it thrown? (5 pt) 4. A 1000-kg elevator is rising and its speed is increasing at 3 m/s2. What is the tension in the elevator cable? (5 pt) 5. A steel ball is dropped from a buildingβs roof and passes a window, taking 0.5 s to fall from the top to the bottom of the window, a distance of 4.9 m. It then falls to the ground. The time the ball spends below the bottom of the window is 1.125 s. How tall is the building? (15 pt) 6. If 2ππβ + 3πποΏ½β = ππβ, ππβ + 2πποΏ½β = 3ππβ, and ππβ = 3iΜ + 2jΜ, then what are ππβ and πποΏ½β? (10 pt) 7. In a soccer match, a player A is running due north toward the goal with a speed of 8 m/s relative to the ground. Other player B passes the ball to him. The ball has a speed of 12 m/s and is moving in a direction 45° east of north, relative to the ground. What are the magnitude and direction of the ballβs velocity relative to the player A? (5 pt) 8. A soccer kicker gives the ball an initial speed of 25 m/s with the elevation angle of 30°. If the ball hits the upper horizontal goalposts bar that is 3.44 m above the ground, find his kicking positions i.e. the ground distance from the goalposts. Ignore the air friction. (15 pt) 9. An interstellar ship has a mass of 1.2×106 kg and is initially at rest relative to a star system. (a) What constant acceleration is needed to bring the ship up to a speed of 0.10ππ (where ππ is the speed of light, 3.0×108 m/s) relative to the star system in 3.0 days? (b) What is that acceleration in ππ units? (c) What force is required for the acceleration? (d) If the engines are shut down when 0.10ππ is reached (the speed then remains constant), how long does the ship take (start to finish) to journey 5.0 light-months, the distance that light travels in 5.0 months? (15 pt) 10. A 5.00-kg box that is several hundred meters above the surface of the earth is suspended from the end of a short vertical rope of negligible mass. A time-dependent upward force is applied to the upper end of the rope, and this results in a tension in the rope of ππ(π‘π‘) = ππππ with ππ = 49 N/s. The box is at rest at π‘π‘ = 0. The only forces on the box are the tension in the rope and gravity. (a) What is the velocity of the box at π‘π‘ =1 s? (b) What is the maximum distance that the box reaches below its initial position? (c) At what value of π‘π‘ does the box return to its initial position? (15 pt)