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Basic kinematic problems: Speed, velocity, degrees, distance

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Problem 4: The pilot of an aircraft wishes to fly due west in a wind blowing at 55 km/h toward the south. If the speed of the aircraft in the absence of wind is 179 km/h, in what direction (in degrees) should the aircraft head? Use the counter-clockwise from east convention
: (Referring to the previous problem.) What will be the airplane's speed (in km/h) relative to the ground?
Answer = km/hr

Problem 6: A boat heads due east directly across a 129-m wide river. The water flows due south with a speed of 2.4 m/s with respect to the shore. The boat speed with respect to the water is 3.3 m/s. Determine the magnitude of the velocity (in m/s) with respect to the shore.
Answer = m/s

Problem 7: (Referring to the previous problem.) Determine the direction (in degrees) of the velocity with respect to the shore. Use the counter-clockwise from east convention.
Answer = degrees

Problem 8: (Referring to the previous problem.) Determine the distance (in m) that the boat will have traveled downstream when it has reached the opposite shore.
Answer = meters
Tom the cat is chasing Jerry the mouse across a table surface 1.33 m high. Jerry steps out of the way at the last second, and Tom slides off the edge of the table at a speed of 5.44 m/s. How many meters from the bottom edge of the table will Tom strike the floor?
Answer = meters

Problem 10: (Referring to the previous problem.) What is the vertical component of velocity (in m/s) of the cat just prior to hitting the floor?
Answer = m/s

Problem 11: The Aculpulco cliff divers dive from a cliff that is 61.2 m high. The rocks below the cliff extend horizontally outward for 23.7 m. What is the minimum horizontal velocity (in m/s) a diver must have when leaving the cliffs to clear the rocks safely? Assume that the divers take a horizontal leap off the cliff.
Answer = m/s

Problem 12: An airplane is traveling 1023 meters above the ocean at a speed of 150 km/hr. The plane wishes to drop a box of supplies to shipwrecked victims in the water below. In order to have a successful mission, how far horizontally (in meters) from the wreckage site must the plane be when dropping the package?
Answer = meters

Problem 13: A student throws a baseball horizontally out a dorm room window 24.3 m above the ground. Another student standing a distance of 29 m from the dorm building catches the baseball at a height of 1.3 m above the ground. What is the initial velocity (in m/s) of the baseball?
Answer = m/s

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Solution Summary

With good explanation and calculations, the questions are answered.