Activity 1

2.65. Juggling Act. A juggler performs in a room whose ceiling is 3.0 m above the level of his hands. He throws a ball upward so that it just reaches the ceiling. (a) What is the initial velocity of the ball? (b) What is the time required for the ball to reach the ceiling? At the instant when the first ball is at the ceiling, the juggler throws a second ball upward with two-thirds the initial velocity of the first. (c) How long after the second ball is thrown did the two balls pass each other? (d) At what distance above the juggler's hand do they pass each other?2.45. A student throws a water balloon vertically downward from the top of a building. The balloon leaves the thrower's hand with a speed of 6.00 m/s. Air resistance may be ignored, so the water bal- loon is in free fall after it leaves the thrower's hand. (a) What is its speed after falling for 2.00 s? (b) How far does it fall in 2.00 s? (c) What is the magnitude of its velocity after falling 10.0 m?2.39. (a) If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground? (b) How long is it in the air?2.76. Egg Drop. You are on the roof of the physics building 46.0 m above the ground (Fig. 2.49). Your physics profes- sor, who is 1.80 m tall, is walk- 46.0 m ing alongside the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your 0 = 1.20 m/s professor's head, where should the professor be when you 1.80 m release the egg? Assume that the egg is in free fall.At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.20 m/s'. At the same instant a truck, traveling with a constant speed of 20.0 m/s, overtakes and passes the car. (a) How far beyond its starting point does the car overtake the truck? (b) How fast is the car traveling when it overtakes the truck?2.67. Large cockroaches can run as fast as 1.50 m/s in short bursts. Suppose you turn on the light in a cheap motel and see one scurry- ing directly away from you at a constant 1.50 m/s. If you start 0.90 m behind the cockroach with an initial speed of 0.80 m/s toward it, what minimum constant acceleration would you need to catch up with it when it has traveled 1.20 m, just short of safety under a counter?The graph in the figure shows the velocity of a motorcycle police officer plotted as a function of time. (a) How far does the officer go in the first 5 s? The first 9 s? The first 13 s? (b) Graph x vs. t and a vs. t. u. (m/s) 50 45 40 2 4 6 8 10 12 14 ()\f