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PreAP Physics Projectiles Worksheet Horizontal launches -- See tutorial and examples in Lesson 2 (part e) of Vectors: Motion and Forces in Two Dimensions from the Physics Classroom Tutorial. 1) A penguin running (maybe waddling?) 1.6 m/s dives out horizontally from the edge of a glacier and reaches the water below 3.0s later. How high was the vertical face of the glacier and how far from its base did the penguin hit the water? (44.1 m, 4.80 m) 2) A lemming takes off from the roof of a building 56m tall and lands 45m from the base. What was the lemming’s initial speed? (13.3 m/s) 3) A giant slingshot launches a box of yesterday’s leftover “chicken nuggets” horizontally at 22.2 m/s from the roof of a building and lands 36.0m from the base of the building. How high is the building? (12.9 m) 4) The pilot of an airplane traveling 160 km/h wants to drop supplies to flood victims isolated on a patch of land 125 m below. The supplies should be dropped how many seconds before the plane is directly overhead? How far forward from where they were released did the supplies land? (5.05 s, 224 m) Vector Components and Resolution -- See tutorial and examples in Lesson 1 (parts d & e) AND Lesson 2 (part d) of Vectors: Motion and Forces in Two Dimensions from the Physics Classroom Tutorial.) Draw a vector diagram for each problem! 5) What are the horizontal and vertical components of a velocity of 32 m/s directed at 25o? (29.0 m/s, 13.5 m/s) 6) Starting from the center of town, a car travels east for 80.0 km and then turns due south for another 192 km, at which point it runs out of gas. Determine the displacement of the stopped car from the center of town. o (208 km, 292 ) 7) A bug starts at point A, crawls 8.0 cm east, then 5.0 cm south, 3.0 cm west, and 4.0 cm north to point B. What is o the total distance traveled? What is the displacement from point A? (20 cm; 5.10 cm, 349 ) 8) What displacement at 70 degrees has an x-component of 450 m? What is the y – component? (1.32 x 103 m or 1.32 km, 1.24 x 103 m or 1.24 km) 9) A plane flies due east from San Francisco to Washington, D.C., a displacement of 5600 km. He then flies from o Washington to Boston, a displacement of 900 km at an angle of 35 (north of east). What is the total displacement o of the plane? (6.36 x 103 km, 4.66 ) Launches at angles (where y = 0 ) -- See tutorial and examples in Lesson 2 (part f) of Vectors: Motion and Forces in Two Dimensions from the Physics Classroom Tutorial. 10) A joyful physics student pitches a sack of dirty gym socks into the air with an initial velocity of 24.5 m/s at 36.9° above the horizontal. Find the: a) total time the sack is in the air. (3.0 s) b) horizontal distance traveled. (58.8 m) c) time when the sack is at maximum height. (1.5 s) d) maximum height the sack reaches. (11.04 m) e) velocity of the sack as it hits the ground. (24.5 m/s, 36.9°below the horizontal) 11) An athlete executing a long jump leaves the ground with a speed of 9.4 m/s at 30o to the horizontal. How far was the jump? If the athlete were to leave the ground at the complementary angle, how far would the jump be? (7.81 m, 7.81 m (make sure to prove it!)) 12) A marmot is fired (that’s not very nice!) with an initial speed of 75.2 m/s at an angle of 34.5 degrees above the horizontal on a long flat firing range. Determine the maximum height reached by the marmot, the total time in the air, and the total horizontal distance covered (that is, the range). (92.6 m, 8.69 s, 539 m) Launches at angles (where y 0 and other challenges) 13) A shot-putter throws the shot with an initial speed of 14 m/s at a 40-degree angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete’s hand at a height of 2.2m above the ground. (22.0 m) 14) A hose lying on the ground shoots a stream of water upward at an angle of 40 degrees to the horizontal. The speed of the water is 20 m/s as it leaves the hose. How high up will it strike a wall that is 8.0 m away? (5.38 m) 15) A box of yesterday’s “chicken nuggets” is projected downward at an angle of 30 degrees below the horizontal from the top of a building 170 m tall. Its initial speed is 40 m/s. How long will it take before striking the ground? How far from the foot of the building will it strike? (4.19 s, 145 m) 16) A fire hose held at ground level shoots water at a speed of 6.5 m/s. At what angle(s) should the nozzle point in order that the water land 2.0 m away? What do you notice about the two angles? (14o, 76o) 17) Your faithful physics teacher is on a dirt bike approaching a creek bed that is 7.0 m wide. A ramp with an incline of 10 degrees has been built for daring (crazy) people who try to jump the creek. Y. F. P. T. is traveling at the bike’s maximum speed, 40 km/h. (a) Should Y. F. P. T. attempt the jump or emphatically hit the brakes? What is the minimum speed the bike must have to make this jump? (hit the brakes! 51.0 km/h) Recommended reading from Essential Physics by Hsu: Chapter Six (No Forces): Projectile Motion, p. 168-191 o Review Questions p. 205 # 104-105, 107-113 Recommended reading from The Physics Classroom (www.physicsclassroom.com) Physics Tutorial – Vectors: Motion and Forces in Two Dimensions – Lesson 1 & especially Lesson 2 The Review Session – Vectors and Projectiles – emphasize projectile questions & problems in your review Recommended viewing from Khan Academy (www.khanacademy.org/#physics) This time, I recommend viewing these AFTER our class discussion and examples. Some of the conventions and approaches Sal uses are different than what we’ll use. Also, he doesn’t have an example of a horizontally launched projectile. So, think of these as review…but can you solve the same problems using our techniques? Also, for those of you that like a challenge, Sal has several more videos not listed here on projectiles that are more advanced (AP level). 1. 2. 3. 4. 5. 6. 7. Visualizing Vectors in 2 Dimensions Projectile at an Angle Different Way to Determine Time in Air Launching and Landing on Different Elevations Total Displacement for Projectile Total Final Velocity for Projectile Correction to Total Final Velocity for Projectile