English Channel and Resultant Displacement
An ostrich cannot fly, but it is able to run fast. Suppose an ostrich runs east for 7. 985 s and then runs 161 m south, so that the magnitude of the ostrich’s resultant displacement is 226 m. Calculate the magnitude of the ostrich’s eastward component and its running speed to the east. 1. Kangaroos can easily jump as far as 8. 0 m. If a kangaroo makes five such jumps westward, how many jumps must it make northward to have a northwest displacement with magnitude of 68 m? What is the angle of the resultant displacement with respect to north? . In 1926, Gertrude Ederle of the United States became the first woman to swim across the English Channel. Suppose Ederle swam 25. 2 km east from the coast near Dover, England, then made a 90o turn and traveled south for 21. 3 km to a point east of Calais, France. What was Ederle’s resultant displacement? 3. Cheetahs are, for short distances, the fastest land animals. In the course of a chase, cheetahs can also change direction very quickly. Suppose a cheetah runs straight north for 5. 0 s, quickly turns and runs 3. 0 x 102 m west. If the magnitude of the cheetah’s resultant displacement is 3. 35 x 102 m, what is the cheetah’s displacement and velocity during the first part of its run? 4. The largest variety of grasshopper in the world is found in Malaysia. These grasshoppers can measure almost a foot in length and can jump 4. 5m. Suppose one of these grasshoppers starts at the origin of a coordinate system and makes exactly eight jumps in a straight line that makes and angle of 35o with the positive x-axis.
Find the grasshopper’s displacements along the x and y axes. 5. The landing speed of the space shuttle Atlantis is 347 km/h. If the shuttle is landing at an angle of 15. 0o with respect to the horizontal, what are the horizontal and vertical components of its velocity? 6. The fastest propeller-driven aircraft is the Russian TU-95/142, which can reach a maximum speed of 925 km/h. For this speed, calculate the plane’s resultant displacement if it travels east for 1. 50 h, then turns north and travels for 2. 00 h. 7.
The longest shot in a golf tournament was made by Mike Austin in 1974. The ball went a distance of 471 m. Suppose the ball was shot horizontally off a cliff at 80. 0 m/s. Calculate the height of the cliff. 8. What would be the initial speed of a projectile that is launched from a cliff 210 m high and hits the ground 420 m away from the cliff? 10. The world’s largest flowerpot is 1. 95 m high. If you were to jump horizontally from the top edge of this flowerpot at a speed of 3. 0 m/s, what would your landing speed be?