You are working as an assistant to an air-traffic controller at the local airport, from which small airplanes take off and land. Your job is to make sure that airplanes are not closer to each other than a minimum safe separation distance of 2.00 km. You observe two small aircraft on your radar screen, out over the ocean surface. The first is at altitude 800 m above the surface, horizontal distance 19.2 km. and 25.0° south of west. The second aircraft is at altitude 1 100 m, horizontal distance 17.6 km, and 20.0° south of west. Your supervisor is concerned that the two aircraft are too close together and asks for a separatism distance for the two airplanes. (Place the x axis west, the y axis south, and the z axis vertical.)
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Chapter 3 Solutions
Physics for Scientists and Engineers
- A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.arrow_forwardGrade 11 Physics: I haven't yet learned the range formula but don't know how to adjust the angle to hit the target by using the formulas I have used. A water balloon is fired at 34.0 m/s from a water cannon, which is aimed at an angle of 18° above the ground. The centre of the cannon’s target (which has a radius of 1.0 m) is painted on the asphalt 42.0 m away from the water cannon. Will the balloon hit the target? Justify your response with calculations that indicate where the water balloon will land and make one suggestion about how to adjust the water cannon so that the water balloon will hit the target. sin??θ=opphyp sin??θ=v⃗yv⃗ v⃗y=v⃗sinθ =(34.0m/s)sin 18° =10.5m/s[up] cosθ=adjhyp cosθ=v⃗xv⃗ v⃗x=v⃗cosθ =(34.0m/s)cos 18° =32.3m/s[forward] Let [up] be positive Δd⃗=0 a⃗=-9.8m/s2[down] v⃗y1=10.5m/s[up] Δt= ? Δd⃗=v⃗y1Δt+12a⃗(Δt)2 0=(10.5m/s)Δt+12(-9.8m/s2)(Δt)2 0=(10.5m/s)Δt-4.9m/s2(Δt)2 0=Δt (10.5m/s-4.9m/s2Δt) Δt=0 or Δt=2.14s v⃗x=32.3m/s [forward] Δt=2.14s Δd⃗x= ?…arrow_forwardPart (A). You are designing the radar system to track the UFOs appearing in the city.In your setup, you have two radars R1 and R2, that are 20 miles from each other. And this happens! Oneday the radars detect a UFO somewhere between them. According to the data provided, the angle ofelevation measured by R1 is 35 degrees. The angle of elevation measured by R2 is 15 degrees. What isthe elevation of the UFO? Round your answer to the nearest thousandth mile. Part (B). Now, one of your radar stations is broken. So you have only one radar. The workingradar suddenly detects another UFO. According to the data provided, the angle of elevation of the UFOfrom some point A on the ground is 60 degrees.After flying 15 seconds horizontally, the angle of elevationchanges to 30 degrees.Also, it is detected by your working radar that the UFO is flying at a speed of 200 m/s,can you find the elevation (height) at which the UFO is flying?Round your answer to the nearest thousandth meter.arrow_forward
- Displacement d1 is in the yz plane 59.9° from the positive direction of the y axis, has a positive z component, and has a magnitude of 3.39 m. Displacement d2 is in the xz plane 20.8° from the positive direction of the x axis, has a positive z component, and has magnitude 1.02 m. What is the angle between d1 and d2?arrow_forwardE N Radar "dish" A radar station detects an airplane approaching directly from the east. At first observation, the range to the plane is 384.0 m at 41.0 ° above the horizon. The plane is tracked for another 124.0 ° in the vertical east-west plane, the range at final contact being 795.0 m. What is the magnitude of the displacement of the plane (in meters) during the period of observation?arrow_forwardVector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 37° from the positive x-axis, and vector C is 11.5 units and points along a direction 150°. What is the direction of the resultant with respect to the positive x-axis in degrees? O 55.5° O 133.2 ° O 114.77° O 284 ° O 85.1 ° 青arrow_forward
- The two hot-air balloons in the drawing are 48.2 m and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3° above the horizontal. What is the horizontal distance x between the two balloons? Number i Units 48.2 m 13.3° X 61.0 marrow_forwardYou are spending the summer as an assistant learning how to navigate on a large ship carrying freight across Lake Erie. One day, you and your ship are to travel across the lake a distance of 180 km traveling due north from your origin port to your destination port. Just as you leave your origin port, the navigation electronics go down. The captain continues sailing, claiming he can depend on his years of experience on the water as a guide. The engineers work on the navigation system while the ship continues to sail, and winds and waves push it off course. Eventually, enough of the navigation system comes back up to tell you your location. The system tells you that your current position is 54.0 km north of the origin port and 21.0 km east of the port. The captain is a little embarrassed that his ship is so far off course and barks an order to you to tell him immediately what heading he should set from your current position to the destination port. Give him an appropriate heading angle.…arrow_forwardA surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 114 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is θ = 36.8°. How wide is the river? y= ? An overhead view of a straight, horizontal river, with a tree on the upper-left bank. A point is marked on the lower right bank. The horizontal distance to the tree from the point is labeled x, and the vertical distance from the tree across to the opposite bank is labeled y. The angle between the horizontal lower bank and a line segment connecting the point and the tree is labeled θ.arrow_forward
- A wonderful hospital nurse on her first day of the job is checking on a variety of patients. Consider the nursing station to be her point of origin. She first travels 100 meters in a direction 37 degrees North of East to check on her first patient. she then travels 49.3 meters due North to check on her second patient. Finally she travels 50 meters due West to check on her third patient. Consider the North direction to be along the y coordinate and the East direction to be along the x coordinate. What is the y coordinate (i.e., in the North direction) in meters of the nurse's net displacement from the nurse's station (the origin)?arrow_forwardVector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 37° from the positive x-axis, and vector C is 11.5 units and points along a direction 150°. What is the direction of the resultant with respect to the positive x-axis in degrees? 55.5o 284 133.2 ° O 114.77 ° 85.1 °arrow_forwardThe vector difference between Vectors A and B is 223.606 N, 26.57° N of W or 223 606 N, 63.43° NW. If the first vector is 100N, due North, what is the real magnitude and direction of Vector A?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning