1) A plane flies 452 km east from city A to city B in 40.0 min and then 804 km south from city B to city C in 1.20 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east).
2) A soccer ball is kicked from the ground with an initial speed of 19.8 m/s at an upward angle of 48.4˚. A player 51.8 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Neglect air resistance.
3) A ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.70 s later, at distance d=26.0 m from the building and at angle Θ=66.0° with the horizontal. (a) Find h. (Hint: One way is to reverse the motion, as if on videotape.) What are the (b) magnitude and (c) angle relative to the horizontal of the velocity at which the ball is thrown (positive angle for above horizontal, negative for below)?
4) A boat is traveling upstream at 10 km/h with respect to the water of a river. The water is flowing at 7.0 km/h with respect to the ground. What are the (a) magnitude and (b) direction of the boat’s velocity with respect to the ground? A child on the boat walks from front to rear at 6.0 km/h with respect to the boat.What are the (c) magnitude and (d) direction of the child’s velocity with respect to the ground?
5) A suspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.50 s. Then security agents appear, and the man runs as fast as he can back along the sidewalk to his starting point, taking 10.1 s. What is the ratio of the man's running speed to the sidewalk's speed?
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