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Chapter 9: Q. 41 (page 603)
Find each quantity if v=3i-5j and w=-2i+3j then 2v+3w
2v+3w=-1j
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In Problems, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box.
Finding the Actual Speed and Direction of an Aircraft A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles per hour (mi/hr) headed due north. The jet stream is 100 mi/hr in the northeasterly direction.
(a) Express the velocity of the 747 relative to the air and the velocity of the jet stream in terms of i and j.
(b) Find the velocity of the 747 relative to the ground.
(c) Find the actual speed and direction of the 747 relative to the ground.
Ground Speed and Direction of an Airplane An airplane has an airspeed of 500 kilometers per hour bearing . The wind velocity is in the direction . Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?
Force Vectors A child pulls a wagon with a force of 40 pounds. The handle of the wagon makes an angle of with the ground. Express the force vector F in terms of i and j.
Ramp Angle Billy and Timmy are using a ramp to load furniture into a truck. While rolling a 250-pound piano up the ramp, they discover that the truck is too full of other furniture for the piano to fit. Timmy holds the piano in place on the ramp while Billy repositions other items to make room for it in the truck. If the angle of inclination of the ramp is how many pounds of force must Timmy exert to hold the piano in position?
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