Vectors in Trigonometry Practice Questions
Read the following study guide for a concept review:
Find the endpoint of each vector if it starts at the origin.
|1.||length 70, angle 79°|
|2.||length 30, angle 308°|
|3.||length 68.4, angle 195.2°|
|4.||length 400, 10° north of west|
|5.||length 141, 21° west of south|
Find the length and direction of the vector from the origin to the given point.
Suppose the person in Figure 16.13 is trying to pull the heavy object with F pounds of force at an angle of θ from the horizontal. Find the component of the force that is going toward sliding the object across the floor.
|11.||θ = 20°, F = 150 pounds|
|12.||θ = 5°, F = 80 pounds|
|13.||θ = 60°, F = 200 pounds|
|14.||θ = 37°, F = 180 pounds|
|15.||θ = 8.6°, F = 130 pounds|
Suppose a weight of W pounds is set on a ramp with angle θ, as illustrated in Figure 16.14. How much of the weight is going down the slope?
|16.||W = 100 pounds, θ = 15°|
|17.||W = 200 pounds, θ = 18°|
|18.||W = 40 pounds, θ = 42°|
|19.||W = 1,000 pounds, θ = 5°|
|20.||W = 100 pounds, θ = 87°|
|21.||Suppose a person walks 30 meters north and then 44 meters northwest. What is the final distance and direction from the starting point?|
|22.||A boat travels 14° north of east for 16 miles, and then 19° north of east for 20 miles. How far is the boat from where it started?|
|23.||A hiker travels 25° south of west for 4 miles and then 10° north of west for 3 miles. In which direction should she head if she wants to go directly back to where she started?|
|24.||A car is being driven through the desert. It goes for 12 miles in the direction 5° south of east. Then the car is turned and driven for 20 miles heading 7° north of east. Finally, it is driven for 9 miles heading 30° north of east. How far is it from where it started? In what direction is it from where it started?|
|25.||Suppose two people are pulling on a heavy statue. One of them pulls with 180 pounds of force and the other with 120 pounds of force. The angle between the two people is 25°. With how much force is the statue being pulled in the direction of its movement? What is the direction of its movement?|
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