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- One morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? From her friend’s location, how far and in what direction should Connie walk to finally get to the store?A windshield wiper rotates through a 120° angle as it cleans a windshield. From the point of rotation, the wiper blade begins at a distance of 4 in. and ends at a distance of 18 in. (The wiper blade is 14 in. in length.) Find the area cleaned by the wiper blade. 18"The measured distance on the ground between two points is 6.85 km. If the corresponding distance between the same points on the map is 13.70 m, the scale of the map is O 1:50000 O 1:500000 O 1:5000 O 1:50 O 1:500
- Satellites When satellites observe Earth, they can scanonly part of Earth’s surface. Some satellites have sensors thatcan measure the angle shown in the figure. Let h representthe satellite’s distance from Earth’s surface, and let r representEarth’s radius. (a) Show that $h=r(\csc \theta-1)$.(b) Find the rate at which $h$ is changing with respect to $\theta$ when$$\theta=30^{\circ} . \text { (Assume } r=4000 \text { miles. })$$in the cartesian plane , we have 40 units for vertical forces and 50 units for horizontal forces.what is the angle theta of the planeFigure shows a wheel rotating about O₂. Two points A and B located along the radius of wheel have speeds of 80 m/s and 140m/s respectively. The distance between the points A and B is 300 mm. The diameter of the wheel (in mm) is 002 OF B
- A hiker leaves the camp, and using the compass, walks 4 km E, then 10 km S, 6 km E, 7 km N, 12 km W, and finally 10 km N. After three days, the hiker goes astray. Using a diagram, find all the sides and angles after the hiker's walk. Remember to make the diagram and identify the vectors.To find the width of a river, a surveyor sets up a transit at point C on one riverbank and sights directly across to point B on the other bank. The surveyor then walks along the bank for a distance of 275 meters to point A. The angle CAB is 57 degrees 28 minutes (57°28’). What is the approximate width of the river? (20-points) 57 28' A 275 mA projectile is aimed to hit a mark in a horizontal plane, but falls short by 20m, when the angle of projection is 20°. However, when projected at 45°, it overshoots by 40m. Determine the angle of projection required to hit the target precisely? Also find the actual distance of the target. ANS: X = a =
- One morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Ans. 667.54 ft, 21.79o N of E) From her friend’s location, how far and in what direction should Connie walk to finally get to the store? (Ans. 1133.08 ft, 33.83o S of W)Draw the projection of the following points on a common reference line 1. Point R is on the VP, 40 mm above HP. 2. Point T is 25 mm above HP, 40 mm behind VP. 3. Point N is on the HP, 35 mm behind VP. 4. Point M is 35 mm below HP, 25 mm behind VP. 5. Point A is 40 mm below HP, 30 mm in front of VP.One morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Answer: 667.54 ft, 21.79o N of E)