Part C - Two Dimensions (please include a diagram for each ...



Name:_________ _________Date:________________Block:______righttopUnit 1: Vector Kinematics Problem SetPart A – Constant Velocity in One Dimension (no diagrams needed)1. Find the average speed for a marathon (42 km) completed in 2 hours, 3 minutes and 2 seconds (the world record as of 2011).2. A car is driven at 80 km/h for 30 min, 100 km/h for 12 min, and 40 km/h for 45 minutes. Find the average speed and total distance.3. A person takes a trip driving at a constant speed of 91 km/h except for a 22 min rest stop. The average speed including the stop is 78 km/h. How long was the trip? (Hint: start with the equation vav= total distancetotal time.)4. Car A leaves Springfield at noon heading west at 88 km/h and car B leaves Mudville at 1:15 pm going 66 km/h due east. If the cars pass each other at 3:11 PM, how far apart are Springfield and Mudville?41071801225555. Referring to the position vs. time graph given, find the velocity at a) 5 secondsb) 11 secondsc) 30 secondsd) 40.7 secondse) What is the acceleration at 25 seconds?f) During which time interval is the object moving forwards?6.?The position-time graph for a particle 403669526670moving along the z-axis is as shown.a) Determine whether the velocity is positive, negative, or zero at times t1, t2, t3, and t4b) Determine whether the acceleration is positive, negative, or zero at times t1, t2, t3, and t4Answers:5.7 m/s = 20.5 km/h62 km/h = 17.2 m/s 2.57 h407.7 kma) 6 m/sb) 0 m/sc) -4 m/s d) 2.7 m/s e) 0 m/s2 f) From 0 to 10 seconds and from 40 to 55 seconds. a) 0, -, +, 0b) -, 0, +, 0 Part B - Constant Acceleration in One Dimension (no diagrams needed)1. The Starship Enterprise can reach half the speed of light in 15 seconds. What acceleration is required?2. A car accelerates uniformly from 33 km/h to 65 km/h over a 150 m distance. What is the car’s acceleration?3. A car accelerates from an initial velocity of 32 km/h, reaching a final velocity of 66 km/h 2.5 seconds later. Find the distance travelled.4. A car has a stopping distance of 35 m from an initial speed of 25 km/h. Find the stopping distance of the same car on the same road if the initial velocity is 75 km/h.5. What is the minimum length of runway required for a Cesna aircraft that takes off at 120 km/h and is capable of a maximum acceleration of 13.2 m/s2?6. A train 400 m long moves at 83.7 km/h. When the front end of the train enters a crossing, the engineer applies the brakes, and, later, the back of last car of the train enters the crossing at 25 km/h. How long did the train block the crossing?7. A rock is dropped into a deep mine shaft and a splash is heard 4.5 seconds later. How deep is the shaft? Assume the speed of sound is 340 m/s and ignore air friction.8. A rocket accelerates upwards from rest at 15 m/s2 for 5 seconds until the fuel runs out. Find the maximum height reached by the rocket.9. A runner in a 100 m race accelerated uniformly over the first 30 m, reaching a final maximum speed of 12 m/s. What is his time for the race?10. A hot air balloon is traveling vertically upward at a constant speed of 7.00 m/s. When it is 21.0 m above the ground, a package is released from the balloon.(a)?After it is released, for how long is the package in the air?(b)?What is its velocity just before impact with the ground?(c)?Repeat?(a) and?(b)?for the case of the balloon?descending?at 5.0 m/s.Answers:1.1.0x107 m/s2 2.0.807 m/s23.34m4.315m5.42.1m6.26.5s7.88.1 m (you must find exactly this answer - "close" answers may be obtained through erroneous methods)8.474.5m9.10.8s10.a) 2.9sb) 21.5m/sc) 1.62s, 20.9m/sPart C - Two Dimensions (please include a diagram for each problem)1. A lime green Smart car is driven (horizontally) off a cliff with an initial velocity of 54 km/h, and it lands 47 m from the base of the cliff. Find:a) the height of the cliffb) the velocity of the car at impactc) the velocity of the car 1.0 seconds after it leaves the cliffd) the vertical component of the car’s acceleratione) the horizontal component of the car’s velocity 0.6 seconds before impactf) the height of the car above the ground when it is 17 m from the cliff, measured horizontally.2. A projectile is launched at 35.0° above horizontal with an initial velocity of 120 m/s. a) Find the horizontal and vertical components of the initial velocity.b) What is the vertical component of the projectile’s velocity 3.00 seconds later?c) What is the projectile’s speed 3.00 s later?d) When is the projectile 67 m above the ground?e) What is the velocity of the projectile at maximum height?f) What is the maximum height reached by the projectile?3. A soccer ball is kicked down the field. It spends 3.2 seconds in the air and lands 64 m away. Find:a) the initial velocity of the ballb) the maximum height reached by the ballc) the height of the ball when it is 20 m downfield.4. A 1.50 kg projectile is launched at 18.0 m/s from level ground. The launch angle is 26.0° above the horizontal. (Assume negligible friction.)a) What is the maximum height reached by this projectile? b) How fast will the projectile be travelling when it is at its maximum height? 5. A stunt vehicle leaves a ramp inclined at 28o to the horizontal with a speed of 35 m/s at a height of 52 m above level ground. Air resistance is negligible.a) What are the vehicle’s vertical and horizontal velocity components as it leaves the incline?b) What is the vehicle’s time of flight? c) What is the vehicle’s range? d) How high above the ground is the vehicle when its horizontal displacement is 60m? 6. A rock is thrown from a cliff top at 18 m/s, 25° above the horizontal. It lands on the beach 4.2 s later.a) What is the height of the cliff? b) How far from the base of the cliff did the rock land? c) When was the speed of the rock 12 m/s?d) How high was the rock above the beach when it was going 21 m/s?e) What was the angle of impact?7. An aircraft heads due south with a speed relative to the air of 44 m/s. Its resultant speed over the ground is 47 m/s. The wind blows to the west.a) What is the speed of the wind? b) What is the direction of the aircraft’s path over the ground? 8. A boat shown below travels at 4.2 m/s relative to the water, in a river flowing at 2.8 m/s. a) At what angle ??must the boat head to reach the destination directly across the river?b) If it takes the boat 3.0 minutes to cross, how wide is the river?c) If the boat were instead to head straight across the river, allowing the current to carry it downstream, how far downstream would it land?9. An airplane is steered toward the Northwest in a wind blowing at 80 km/h towards the North. The plane’s speed relative to the air is 190 km/h. a) Find the velocity of the plane relative to the ground.b) What direction should the plane be pointed do that it travels due East?Answers:a) 48.1m b) 34.2m/s 64.0 c) 17.9m/s 33.2 d) -9.8m/s2 e) 15m/s f) 41 ma) H: 98.3m/s V: 68.8m/s b) 39.4m/s c) 105.9m/s d) 1.1s, 12.8s e) 98.3m/s f) 241.5ma) 25.4m/s 38.1 b) 12.5m c) 10.8m a) 3.2m b) 16.2m/sa) H: 30.9m/s V: 16.3m/s b) 5.3s c) 164.9m d) 65.4m a) 54.5m b) 68.5m c) Never d) 49m e) 64.1a) 16.5m/s b) 20.6 West of South or 69.4 South of West a) =41.8 b) 563m c) 376ma) 253km/h 32 West of North or 58 North of West b) 24.9 South of East or 65.1 East of South ................
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