Honors Physics HW Mixed Review of 2-D Motion

Transcription

1 Honors Physics HW Mixed Review of -D Motion Name Date. In 974, Mike Austin shot the longest shot on a golf tournament. The ball went a distance of 47 m. Suppose the ball was shot horizontally off a cliff at 80.0 m/s. How long was the ball in the air? What is the height of the cliff? 𝑣! = 80.0! 𝑥 = 47 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 𝑥 𝑣! 𝑡 𝑥 47 = 𝟓. 𝟖𝟗 𝒔𝒆𝒄𝒐𝒏𝒅𝒔 𝑣! 80.0 𝑎! 𝑡! = 9.8! (5.89 )! = 𝟏. 𝟕𝟎 𝒙 𝟏𝟎𝟐 𝒎. A Snorkel fire engine is designed for putting out fires that are well above street level. The engine has a hydraulic lift that lifts the firefighter and a system that delivers pressurized water to the firefighter. Suppose that the engine cannot move closer than 5 m to a building that has a fire on its sixth floor, 35 m above street level. Also assume that the water nozzle is stuck in the horizontal position (an improbable situation). If the horizontal speed of the water emerging from the hose is 5 m/s, how high above the street must the firefighter be lifted in order for the water to reach the fire? 𝑣! = 5! 𝑥 = 5 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 𝑥 𝑣! 𝑡 𝑥 5 = 𝑒𝑐𝑜𝑛𝑑 𝑣! 5 𝑎! 𝑡! = 9.8! (.6666 )! = 4 𝑎𝑏𝑜𝑣𝑒 𝑡ℎ𝑒 𝑓𝑙𝑜𝑜𝑟 𝑜𝑛 𝑓𝑖𝑟𝑒 49 𝑎𝑏𝑜𝑣𝑒 𝑡ℎ𝑒 𝑡𝑟𝑒𝑒𝑡

2 3. For six weeks in 99, Akira Matsushima, from Japan, rode a unicycle more than 3.00 x 0 3 miles across the United States. Suppose Matsushima is riding through a city. If he travels 50.0 m at a 0 o angle, then turns and rides 5.0 m at an angle of 0.0 o what is his resultant displacement? 50.0 m at 0 o x-component = 50.0 m y-component = 0 m x-component = 87.5 m y-component = 08. m 5.0 m at 0.0 o x-component = -6.5 m y-component = 08. m 39 m at 5 o 4. The fastest propeller-driven aircraft is the Russian TU-95/4, which can reach a maximum speed of 95 km/hour. For this speed, calculate the plane s resultant displacement if it travels at an angle of 0 o from.5 hours and then travels for.00 hours at an angle of 35 o. 95 km/hr at 0 o for.5 hrs x = v t x = 95!"!! km.5 hrs x-component = km y-component = 0 km x-component = 79.5 km y-component = 308 km 95 km/hr at 35 o for.00 hrs x = x = v t 95 km hr 850 km.00 hrs x-component = -308 km y-component = 308 m 30 km at 87 o

3 5. Florence Griffith-Joyner of the United States set the women s world record for the 00 m run, running with an average speed of 9.37 m/s. Suppose Griffith-Joyner wants to jump over a river. She runs horizontally from the river s higher bank at 9.37 m/s and lands on the edge of the opposite bank. If the difference in height between the two banks is.00 m, how wide is the river? 𝑣! = 9.37! 𝑥 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛.00 𝑎 𝑡! 𝑦 (.00 ) = 𝑒𝑐𝑜𝑛𝑑 𝑎! 9.8! 𝑥 𝑣! 𝑡 = 𝑒𝑐𝑜𝑛𝑑 𝟓. 𝟗𝟗 𝒎 6. The longest banana split ever made was 7,30 m long (needless to say, more than one banana was used). If the banana split were placed next to Mount Everest at sea level and an archer were to shoot an arrow horizontally from the top of Mount Everest, which is located 8848 m above sea level, would the arrow hit the banana split? Assume that the arrow cannot be shot faster than 00.0 m/s, that there is no air resistance, and that the arrow lands at sea level. 0.0 𝑥 =? (𝑛𝑒𝑒𝑑 𝑖𝑡 𝑡𝑜 𝑏𝑒 𝑙𝑒 𝑡ℎ𝑎𝑛 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 7,30 ) 8848 𝑥 𝑣! 𝑡 = 00.0! 𝑎 𝑡!! 𝑦 ( 8848 ) = 4.49 𝑒𝑐𝑜𝑛𝑑 𝑎! 9.8! 4.49 𝑒𝑐𝑜𝑛𝑑 𝟒𝟐𝟒𝟗 𝒎 𝒘𝒊𝒍𝒍 𝒉𝒊𝒕 𝒃𝒂𝒏𝒂𝒏𝒂 𝒔𝒑𝒍𝒊𝒕 3

4 7. A resultant vector begins at the origin and ends at the point (-5.4 m, -4.9 m). What is the angle and magnitude of the resultant vector? What are the magnitudes of the x and y components of the resultant vector? x-component is -5.4 m y-component is -4.9 m a! + b! = c! Phthagorean Theorem to find length of resultant resultant = ( 5.4 m)! + ( 4.9 m)! = 6 m is in third quadrant because both x and y component are negative. Using tangent can find the angle and then need to add it to 80 to find angle using convention. opp adj = angle resultant is 6 m at 50 o 4.9 m 5.4 m = 70 degrees, add to 80 angle is 50 degrees 8. An ostrich cannot fly, but it is able to run fast. Suppose an ostrich runs east for 7.95 s and then runs 6 m south, so that the magnitude of the ostrich s resultant displacement is 6 m. Calculate the magnitude of the ostrich s eastward component and its running speed. x-component unknown is 6 m y-component is -6 m Use Pythagorean theorem to find x-component (59 m) Speed = distance/time Speed = 59 m/7.95 s = 0.0 m/s 9. The pronghorn antelope, found in North America, is the best long-distance runner among mammals. It has been observed to travel at an average speed of more than 55 km/h over a distance of 6.0 km. Suppose the antelope runs a distance of 5.0 km in a direction.5 degrees, turns and then runs.0 km south. Calculate the resultant displacement. 5.0 km at.5 o x-component = 4.9 km y-component =.0 km x-component = 4.9 km y-component = 0 km.0 km South x-component = 0 km y-component = -.0 km 4.9 km at 0 o 4

5 0. Kangaroos can easily jump as far as 8.0 m. If a kangaroo makes five such jumps westward, how many jumps must it make northward to have a displacement of 68 m? What is the angle of the resultant displacement? 5 jumps at 8.0 m, West x-component = -40. m 68 m y-component = 0 m Use Pythagorean Theorem to find north component x-component = 0 m y-component = 55 m 55 m North component Angle of resultant in second quadrant so need to find the angle and then subtract from 80 opp adj = angle 55 m 40. m = 54 degrees, subtract from 80 angle is 6 degrees 5