tutorial_1 - Mechanics tutorial_1 1 A surveying instrument...

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Mechanics tutorial_1.doc 1 1. A surveying instrument for measuring distance and angle is located at C, point A is at an elevation of 9.2 above the horizontal plane (x-y plane). The instrument has to rotate about the vertical axis through 41 from the x direction in order to align with A. The distance from C to A is 5005m. Corresponding values for point B are 1.3 , 73.4 and 7037m. Determine (a) the locations of points A and B in Cartesian co-ordinates relative to C, (b) the distance from A to B, (c) the distance from A to B projected onto the horizontal plane. ans: (a) (3729, 3241, 800.2)m,(2010, 6742, 159.7)m (b) 3952m (c) 3900m 2. Point C and D are located at (1,2,4)m and (2,-1,1)m respectively. Determine the length of CD and the angle COD, where O is the original of the co-ordinates. ans: 4.36m, 69.12 3. A vector is given by (2i+3j+1k)m. What is the component of this vector (a) in the y-direction and (b) in the direction parallel to the line from A to B, where A is at point (1,1,0)m and B is at (3,4,5)m? ans: 3m, 2.92m 4. What are the angles between the line joining the origin O and a point at (2,-5,6)m and the positive x-, y- and z- axes? ans: 75.6 , 128.3 , 41.9 5. A point on a mechanism has a speed of 5m/s and a tangential acceleration of magnitude 2m/s 2 . If the magnitude of the total acceleration is 3.0m/s 2 , what is the radius of curvature of the path traced by the point at this instant. ans:
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tutorial_1 - Mechanics tutorial_1 1 A surveying instrument...

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