Example 1: Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward) and the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s t = ?? 2 In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. So use this : -8.52 m = (0 m/s)*(t) + 0.5*(-9.8 m/s2)*(t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2)*(t)2 -8.52 m = (-4.9 m/s2)*(t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The initial velocity (vi) of the vase is +26.2 m/s vf = 0 m/s a = -9. Determine the height to which the vase will rise above its initial height.6 m/s2)*d = -686. and d.44 m2/s2 d = (-686. The acceleration (a) of the vase is -9.8 m/s2 Diagram: Given: Find: vi = 26.8 m/s d = ?? 2 In this specific case. the three known variables and the one unknown variable are vi.44 m2/s2 (-19. a.6 m/s2)*d (-19.6 m/s2) d = 35.2 m/s)2 + 2*(-9.2 m/s.0 meters before reaching its peak.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.44 m2/s2 + (-19.8m/s2)*d 0 m2/s2 = 686. So use this: (0 m/s)2 = (26.44 m2/s2)/ (-19.6 m/s2)*d = 0 m2/s2 -686.Example 2: Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26. vf. .2 m/s. (The + sign indicates that the initial velocity is an upwards velocity) and the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory. 10 m/s over a distance of 35. An engineer is designing the runway for an airport. b. .8 seconds. A kangaroo is capable of jumping to a height of 2. then what is the acceleration and what is the distance that the sled travels? g.21 seconds for a distance of 110 m. Determine the distance traveled before takeoff. An airplane accelerates down a runway at 3.8 s until is finally lifts off the ground. what is the minimum allowed length for the runway? i.47 seconds.1 m/s in 2.Check Your Understanding a. The acceleration of gravity on the moon is 1.6 seconds. A car starts from rest and accelerates uniformly over a time of 5. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.5 m/s to 46. If Upton free falls for 2. the lowest acceleration rate is likely to be 3 m/s2. Determine the skidding distance of the car (assume uniform acceleration). Of the planes that will use the airport. f.40 meters. The takeoff speed for this plane will be 65 m/s. Rocket-powered sleds are used to test the human response to acceleration. Determine the acceleration of the car and the distance traveled.4 m.20 m/s2 for 32. h. Determine the acceleration of the car. Assuming this minimum acceleration. A bike accelerates uniformly from rest to a speed of 7.62 m. A feather is dropped on the moon from a height of 1.67 m/s 2. Determine the acceleration of the bike. c. what will be his final velocity and how far will he fall? d. Determine the time for the feather to fall to the surface of the moon. Determine the takeoff speed of the kangaroo. Upton Chuck is riding the Giant Drop at Great America.4 m/s skids to a stop in 2. A race car accelerates uniformly from 18. j. A car traveling at 22.55 s. e. A dragster accelerates to a speed of 112 m/s over a distance of 398 m. A plane has a takeoff speed of 88. Determine the acceleration (assume uniform) of the dragster.3 m/s and requires 1365 m to reach that speed. A bullet leaves a rifle with a muzzle velocity of 521 m/s.) n. A stone is dropped into a deep well and is heard to hit the water 3. q. Determine the acceleration of the bullet (assume a uniform acceleration).90 m/s2. The observation deck of tall skyscraper 370 m above the street.840 m. the bullet moves a distance of 0. A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. o. s.k. Determine the depth of the well. m. Determine the acceleration of the plane and the time required to reach this speed.25 s. . Determine the time required for a penny to free fall from the deck to the street below. If Michael Jordan has a vertical leap of 1. It was once recorded that a Jaguar left skid marks that were 290 m in length. determine the speed of the Jaguar before it began to skid.29 m.) p. The bullet penetrates for a distance of 0. Determine the height to which the ball rises before it reaches its peak. r. then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)? l. (Assume a uniform acceleration.41 s after being dropped. (Hint: the time to rise to the peak is one-half the total hang-time. Determine the acceleration of the bullet while moving into the clay. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3. A baseball is popped straight up into the air and has a hang-time of 6. While accelerating through the barrel of the rifle.0621 m. 23 mi/hr) must an object be thrown to reach a height of 91.5 m (equivalent to one football field)? Assume negligible air resistance. . With what speed in miles/hr (1 m/s = 2.t.