## Vectors and Equilibrium, Numerical Problems

S.No | Problem |
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Problem 1 | A 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? See Solution |

Problem 2 | A 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? See Solution |

Problem 3 | A 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. See Solution |

Problem 4 | Find 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. See Solution |

Problem 5 | Vector 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? See Solution |

Problem 6 | The magnitudes of dot and cross product of two vectors are 6√3 and 6 respectively. Find the angle between the vectors? See Solution |

Problem 7 | A 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? See Solution |

Problem 8 | A 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. See Solution |

Problem 9 | The 450 kg uniform i-beam supports the load of 220 kg as shown. Determine the reactions at the supports. See Solution |

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