Science Tutorial: 1 D Kinematics and Vectors
1.32 A rocket blasts off and moves straight upward from the launch pad with constant acceleration. After 3.0 s the rocket is at a height of 77 m. (a) What are the magnitude and direction of the rocket’s acceleration? (b) What is its speed at this time? (17m/s2 up, 51m/s)
1.35 On July 13, 1977, while on a test drive at Silverstone, the throttle on David Purley’s car stuck wide open. The resulting crash subjected Purley to the greatest “g-force” ever survived by a human—he decelerated from 173 km/h to zero in a distance of only about 0.66 m. Calculate the magnitude of the acceleration experienced by Purley (assuming it to be constant), and express your answer in units of the acceleration of gravity, (180g)
1.43 Standing at the edge of a cliff 32.5 m high, you drop a ball. Later, you throw a second ball downward with an initial speed of 11.0 m/s. (a) Which ball has the greater increase in speed when it reaches the base of the cliff, or do both balls speed up by the same amount? (b) Verify your answer to part (a) with a calculation. (25.3m/s, 16.5m/s)
1.44 You shoot an arrow into the air. Two seconds later (2.00 s) the arrow has gone straight upward to a height of 30.0 m above its launch point. (a) What was the arrow’s initial speed? (b) How long did it take for the arrow to first reach a height of 15.0 m above its launch point? (24.8m/s, 0.702s)
1.46 A model rocket blasts off and moves upward with an acceleration of until it reaches a height of 26 m, at which point its engine shuts off and it continues its flight in free fall. (a) What is the maximum height attained by the rocket? (b) What is the speed of the rocket just before it hits the ground? (c) What is the total duration of the rocket’s flight? (58m, 34m/s, 8.1s)
1.47 While sitting on a tree branch 10.0 m above the ground, you drop a chestnut. When the chestnut has fallen 2.5 m, you throw a second chestnut straight down. What initial speed must you give the second chestnut if they are both to reach the ground at the same time? (11m/s)
2.1 Find the x and y components of a position vector, of magnitude if its angle relative to the x axis is (a) 35.0° and (b) 65.0°. (61m, 43m, 32m, 68m)
2.5 Vector has a magnitude of 50 units and points in the positive x direction. A second vector, has a magnitude of 120 units and points at an angle of 70° below the x axis. Which vector has (a) the greater x component, and (b) the greater y component?
2.6 A treasure map directs you to start at a palm tree and walk due north for 12.0 m. You are then to turn 90° and walk 25.0 m; then turn 90° again and walk 5.00 m. Give the distance from the palm tree, and the direction relative to north, for each of the four possible locations of the treasure. (30.2m, 55.8° west of north, 26.0m, 74.4° west of north, 30.2m, 55.8° east of north, 26.0m, 74.4° east of north)
2.8 A vector has a magnitude of 50.0 m and points in a direction 20.0° below the positive x axis. A second vector, has a magnitude of 70.0 m and points in a direction 50.0° above the positive x axis. (a) Sketch the vectors and (b) Using the component method of vector addition, find the magnitude and direction of the vector (99.0m, 21.7°)
2.9 An air traffic controller observes two aeroplanes approaching the airport. The displacement from the control tower to plane 1 is given by the vector which has a magnitude of 220 km and points in a direction 32° north of west. The displacement from the control tower to plane 2 is given by the vector which has a magnitude of 140 km and points 65° east of north. (a) Sketch the vectors and Notice that is the displacement from plane 2 to plane 1. (b) Find the magnitude and direction of the vector (320km, 10° north of west)
2.10 Vector points in the positive x direction and has a magnitude of 75 m. The vector points in the positive y direction and has a magnitude of 95 m. (a) Sketch and (b) Estimate the magnitude and direction of the vector (c) Verify your estimate in part (b) with a numerical calculation. (121m, 128°)