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Chapter 3: Q1CQ (page 118)
Which of the following is a vector: a person鈥檚 height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth鈥檚 population, the acceleration of gravity?
Acceleration due to gravity is only a vector quantity.
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A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west corner, she measures the first side to be \(80.0{\rm{ m}}\) long and the next to be \(105\;{\rm{m}}\). These sides are represented as displacement vectors \({\rm{A}}\) from \({\rm{B}}\) in Figure 3.61. She then correctly calculates the length and orientation of the third side \({\rm{C}}\). What is her result?
In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: north of west; then south of east; then south of west; then straight east; then east of north; then south of west; and finally north of east. What is his final position relative to the island?
A ship sets sail from Rotterdam, The Netherlands, heading due north at m/s relative to the water. The local ocean current is 1.50m/s in a directionnorth of east. What is the velocity of the ship relative to the Earth?
A cloud of dirt falls from the bed of a moving truck. It strikes the ground directly below the end of the truck. What is the direction of its velocity relative to the truck just before it hits? Is this the same as the direction of its velocity relative to ground just before it hits? Explain your answers.
Prove that the trajectory of a projectile is parabolic, having the form . To obtain this expression, solve the equation for and substitute it into the expression for (These equations describe the xand y positions of a projectile that starts at the origin.) You should obtain an equation of the form where a and bare constants.
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