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- In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h, (a) in what direction must the pilot head her plane to move directly north across land and (b) how long does it take her to reach a point 300 km directly north of her starting point?In the control tower at a regional airport, an air traffic controller monitors two aircraft as their positions change with respect to the control tower. One plane is a cargo carrier Boeing 747 and the other plane is a Douglas DC-3. The Boeing is at an altitude of 2500 m, climbing at 100 above the horizontal, and moving 30 north of west. The DC-3 is at an altitude of 3000 m, climbing at 50 above the horizontal, and cruising directly west. (a) Find the position vectors of the planes relative to the control tower. (b) What is the distance between the planes at the moment the air traffic controller makes a note about their positions?
- A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?Starting at the island of Moi in an unknown archipelago, a fishing boat makes a round trip with two stops at the islands of Noi and Poi. It sails from Moi for 4.76 nautical miles (nmi) in a direction 37 north of east to Noi. From Noi, it sails 69 west of north to Poi. On its return leg from Poi, it sails 28 east of south. What distance does the boat sail between Noi and Poi? What distance does it sail between Moi and Poi? Express your answer both in nautical miles and in kilometei. Note: 1 nmi = 1852m.Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by computing its magnitude. If the convoy in Example 2.8 was moving across a desert flatland—that is, it the third component of its velocity was zero—what is the unit vector of its direction of motion? Which geographic direction does it represent?
- 5. A ball is thrown following a projectile motion. It is known that the horizontal distance (range) the ball can travel is given by R = sin 20, where r is the range (in %3D feet), vo is the initial speed (in f/s), 0 is the angle of elevation the ball is thrown, and g=32 ft/s? is the acceleration due to gravity. a. Express the new range in terms of the original range when an angle 8 (0< 0 < 45°) is doubled. xiii b. If a ball travels a horizontal distance of 20 ft when kicked at an angle of a with initial speed of 20V2 ft/s, find the horizontal distance it can travel when you double a. Hint: use result of item (a).1110. In Fig. P-1109, a ball thrown down the incline strikes it at a distance s 254.5 It. If the ball rises to a maximum height h 64.4 ft above the point of release, compute its initial velocity vo and inclination 6. Ans. v. = 80.5 ft per see; 0= 53.1° FIG. P-1109 and P-1110.15. Jake is flying a plane due north at 225 km/h as a wind pushes it due east at 55.0km/h. Find thr magnitude and direction of the plane/s resultant velocity. a) 225 km/h at 76o b) 232 km/h at 76o C) 55 km/h at 00 D) 225 km/h at 00
- 5. A ball is thrown following a projectile motion. It is known that the horizontal %3D distance (range) the ball can travel is given by R = sin 20, where r is the range (in feet), vo is the initial speed (in ft/s), 0 is the angle of elevation the ball is thrown, and g=32 ft/s2 is the acceleration due to gravity. a. Express the new range in terms of the original range when an angle e (0< 0 < 45°) is doubled. b. If a ball travels a horizontal distance of 20 ft when kicked at an angle of a with initial speed of 20/2 ft/s, find the horizontal distance it can travel when you double a. neb Hint: use result of item (a).A person starts from his home and walks the following distances: i) 1500 yards, 50° N of E ii) 1800 yards, 50° W of N ii) 1000 yards, due south. What direction is the person relative to his home? O 38° S of E O 55° N of W O 42° S of W O 27° E of S O 72° N of W Save for Later Submit Answer W 版 )l ASUS prt sc sysro 18 f12 pause break delete home O/R5. A ball is thrown following a projectile motion, it is known that the horizontal distance (range) the ball can travel is given by R= sin 24, where r is the range (in feet), vy is the initial speed (in ft/s), B is the angle of elevation the bal is thrown, and g=32 ft/s? is the acceleration due to gravity. a. Express the new range in terms of the original range when an angle 8 (0< @ < 45°) is doubled. b. If a balt travels a horizontai distance of 20 t when kicked at an angle of a with initial speed of 20/2 fus, find the horizontal distance it can travel when you double z. Hint: use result of item (a).