28. How fast must a ball be thrown upward to reach a height of 12 m? 29. A person dives off the edge of a cliff 33 m above the sur- face of the sea below. Assuming that air resistance is neg- ligible, how long does the dive last and with what speed does the person enter the water! 30. A ball dropped from the roof of a building takes 4 s to reach the street. How high is the building? 31. A ball is thrown downward at 12 m/s. What is its speed 1.0 s later? 32. When will a stone thrown vertically upward at 9.8 m/s reach the ground? 33. A ball is thrown upward from the edge of a cliff with an initial speed of 6 m/s. (a) How fast is it moving 0.5 s later? In what direction? (b) How fast is it moving 2 s later? In what direction? (Consider upward as + and downward as -; then , = +6 m/sandg = -9.8 m/s'.) 34. The air resistance experienced by a falling object is not an important factor until a speed of about half its terminal speed is reached. The terminal speed of a golf ball is 40 m/s. How much time is needed for a dropped golf ball to reach a speed of half this? How far does it fall in this time? 35. A ball is thrown vertically upward with an initial speed of 30 m/s. (a) How long will it take the ball to reach the highest point in its path? (b) How long will it take the ball to return to its starting place? (c) What will the ball's speed be there? 36. A rifle is aimed directly at the bull's-eye of a target 50 m away. If the bullet's speed is 350 m/s, how far below the bull's-eye does the bullet strike the target? 37. An airplane is in level flight at a speed of 100 m/s and an altitude of 1200 m when a windshield wiper falls off. What will the wiper's speed be when it reaches the ground? (Hint: A vector calculation is needed here and in Exercises 38 and 39.)38. A ball is thrown horizontally from the roof of a building 20 m high at 30 m/s. At what speed will the ball strike the ground?39. A bullet is fired horizontally from a rifle at 200 m/s from a cliff above a plain below. The bullet reaches the plain 5 s later. (a) How high was the cliff? (b) How far from the cliff did the bullet reach the plain? (c) What was the bul- let's speed when it reached the plain? 40. An airplane whose speed is 60 m/s is flying at an altitude of 500 m over the ocean toward a stationary sinking ship. At what horizontal distance from the ship should the crew of the airplane drop a pump into the water next to the ship? 41. A person at the masthead of a sailboat moving at con- stant speed in a straight line drops a wrench. The mast- head is 20 m above the boat's deck and the stern of the boat is 10 m behind the mast. Is there a minimum speed the sailboat can have so that the wrench will not land on the deck? If there is such a speed, what is it? 2.9 Second Law of Motion 42. Compare the tension in the coupling between the first two cars of a train with the tension in the coupling between the last two cars when (a) the train's speed is constant and (b) the train is accelerating. (The tension is the magnitude of the force either end of the coupling exerts on the car it is attached to.) 43. In accelerating from a standing start to a speed of 300 km/h (186 mi/h-not its top speed!), the 1900-kg Bugatti Veyron sports car exerts an average force on the road of 9.4 KN. How long does the car take to reach 300 km/h? 44. A 12,000-kg airplane launched by a catapult from an aircraft carrier is accelerated from 0 to 200 km/h in 3 s. (a) How many times the acceleration due to gravity is the airplane's acceleration? (b) What is the average force the catapult exerts on the airplane? 45. The brakes of a 1200-kg car exert a force of 4 kN. How long will it take for them to slow the car to a stop from an initial speed of 24 m/s?46. A force of 20 N gives an object an acceleration of 5 m/s . (a) What force would be needed to give the same object an acceleration of 1 m/s? (b) What force would be needed to give it an acceleration of 10 m/s ? 47. A bicycle and its rider together have a mass of 80 kg. If the bicycle's speed is 6 m/s, how much force is needed to bring it to a stop in 4 s? 48. A 430-g soccer ball at rest on the ground is kicked with a force of 600 N and flies off at 15 m/s. How long was the toe of the person kicking the ball in contact with it? 49. A car and driver with a total mass of 1600 kg has a maxi- mum acceleration of 1.2 m/s . If the car picks up three 80-kg passengers, what is its maximum acceleration now