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Vectors and Equilibrium, Numerical Problems

See here numerical problems on Vectors and Equilibrium included in the new course of First Year Physics.

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Problem 1A person throws a ball straight up with a speed of 12 m/s. If the bus is moving at 25 m/s, what is the velocity of the ball to an observer on the ground?
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Problem 2A football leaves the foot of a punter at an angle of 54° (positive x-direction) at a speed of 21 m/s. Determine the horizontal and vertical components of the velocity?
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Problem 3A 1.84 kg school bag hangs in the middle of a clothesline (طناب), causing it to sag (dip) by an angle θ = 3.50°. Find the tension, T in the clothesline.
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Problem 4Find the magnitude and direction of vector represented by the following pair of components. (a) Ax = -2.3 cm, Ay = 4.1 cm (b) Ax = 3.9 m, Ay = -1.8 m.
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Problem 5Vector F having magnitude 5.5 N makes 10° with x-axis and vector r with magnitude 4.3 m makes 80° with x-axis. What is the magnitude of their dot and scalar products?
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Problem 6The magnitudes of dot and cross product of two vectors are 6√3 and 6 respectively. Find the angle between the vectors?
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Problem 7A uniform rod 1 m long with weight 6 N can be supported in a horizontal position on a sharp edge with weights of 10 N and 15 N suspended from its ends. What is the position of point of balance?
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Problem 8A 4.0 m long ladder with weight of 120 N leans against a wall making 70° above a cement floor as shown in the figure. Assuming the wall is frictionless but the floor is not determine the forces exerted on the ladder by the floor and by the wall.
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Problem 9The 450 kg uniform i-beam supports the load of 220 kg as shown. Determine the reactions at the supports.
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