ACC.D Projectile Motion Horizontally Launched Projectiles Original Assignment

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1 ACC.D Projectile Motion Horizontally Launched Projectiles Original Assignment The following diagram pertains to questions #1 and #2 above. A scale is used where 1 cm = 5 meters. (Note that 1 cm may be a different distance for different computer monitors; thus, a cm-ruler is given in the diagram.) 1. Anna Litical drops a ball from rest from the top of 78.4-meter high cliff. How much time will it take for the ball to reach the ground and at what height will the ball be after each second of motion? A cannonball is launched horizontally from the top of an 78.4-meter high cliff. How much time will it take for the ball to reach the ground and at what height will the ball be after each second of travel? 3. A skier skis horizontally off of a 72 m high cliff at 4.0 m/s. Find a. The amount of time it takes to reach the ground. b. How far away from the base of the cliff he lands. 4. Wile E. Coyote is chasing the Road Runner when he takes a wrong turn and accidentally runs off of a 75 m high cliff. When he leaves the cliff he is running horizontally at 13 m/s. a. How long does it take him to hit the ground below? b. What is his total velocity upon impact? 5. The police are called to the scene of an accident. A car slid off the road and fell into an embankment, crashing into the ground below. The speed limit is 60 km/h and the driver claims that he was not speeding. Use the information below to find the initial velocity at which the car left the road and determine whether the driver is lying or not. Find answer in then covert to 6. A mountain lion leaps horizontally from a 7.5 m high rock with a speed of 4.5 m/s. How far from the base of the rock will he land? 7. A cannon ball is shot from cannon at a height of 15 m with a velocity of 20 m/s. How far away will the cannon ball land? 8. A rock is thrown horizontally from the top of a cliff 98 m high, with a horizontal speed of 27 m/s. (a) For what interval of time is the rock in the air? (b) How far from the base of the cliff does the rock land? (c) With what velocity does the rock hit? 9. A rescue pilot wishes to drop a package of emergency supplies so that it lands as close as possible to a target. If the plane travels with a velocity of 81 m/s and is flying 125 m above the target, how far away (horizontally) from the target must the rescue pilot drop the package?

2 10. A bullet is fired with a horizontal velocity of 330 m/s from a height of 1.6 m above ground. Assuming the ground is level how far from the gun will the bullet hit the ground? 11. A fireman is standing on top of a building 20.0 m high. He finds that if he holds the hose so that water issues from it horizontally at 12 m/s, the water will hit a burning wall of an adjacent building at a height of 15.0 m above the ground. What is the horizontal distance from the fireman to the building? 12. A softball rolls off a 95-centimeter tall table. It strikes the floor 80 centimeters from the base of the table. A. How much time does it spend in the air? t = 0.44 sec B. How fast did it roll off the table? V X = 1.82 m/sec C. How fast was it traveling vertically when it hit the floor? V Y = m/sec D. What was its impact speed when it impacted the floor? This is asking you to calculate V R, the resultant velocity. V R = 4.68 m/sec 13. A student tosses a coin into the pool of a nearby fountain. The coin travels 5 meters forward while taking 1 second before it impacts the water. A. How fast was the coin released horizontally through the air? (Find V X ) V X = 5.0 m/sec B. How high above the top of the fountain's pool did the student release the coin? (Find d Y ) d = +4.9 meters C. How fast was the coin falling vertically just before it struck the water? (Find V Y ) V Y = m/sec D. What was the coin's impact speed, resultant velocity, when it initially entered the water? (Find V R the resultant velocity.) V R = 11.0 m/sec

3 14. An Olympic diver springs forward off a 10 meter platform. He enters the water 8 meters beyond the edge of the platform. A. How much time does it spend in the air? t = 1.43 sec B. How fast did he spring forward off the edge of the diving tower? V X = 5.59 m/sec C. How fast was it traveling vertically when it hit the water? V Y = -14 m/sec D. What was its impact speed when it impacted the water? V R = 15.1 m/sec E. At what angle did he enter the water? 68.2 O 15. A helicopter drops a relief package to some isolated refugees. The package travels 250 meters forward while taking 4 seconds to land after it is released. A. How high was the helicopter flying when it released the package? d = 78.4 meters B. How fast was the helicopter flying when it released the package? V X = 62.5 m/sec C. How fast was the package falling vertically just before it landed on the island? V Y = m/sec D. What was the package's impact speed, resultant velocity, when it landed on the island? V R = 73.8 m/sec At what angle was the package's trajectory with respect to the ground at the instant that it landed? 31.1º

4 Answers 1. It will take 4 seconds to fall 78.4 meters Use the equation y = 0.5 a t 2 and substitute -9.8 m/s/s for a. The vertical displacement must then be subtracted from the initial height of m. At t = 1 s, y = 4.9 m (down) so height is 73.5 m (78.4 m m ) At t = 2 s, y = 19.6 m (down) so height is 58.8 m (78.4 m m ) At t = 3 s, y = 44.1 m (down) so height is 34.3 m (78.4 m - 45 m) At t = 4 s, y = 78.4 m (down) so height is 0 m (78.4 m m) 2. It will still take 4 seconds to fall 78.4 meters Use the equation y = 0.5 g t 2 and substitute -9.8 m/s/s for g. The vertical displacement must then be subtracted from the initial height of m. At t = 1 s, y = 4.9 m (down) so height is 73.5 m (78.4 m m ) At t = 2 s, y = 19.6 m (down) so height is 58.8 m (78.4 m m ) At t = 3 s, y = 44.1 m (down) so height is 34.3 m (78.4 m - 45 m) At t = 4 s, y = 78.4 m (down) so height is 0 m (78.4 m m) NOTE: the cannon ball's horizontal speed does not affect the time to fall a vertical distance of 78.4 m.

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8 7. 8. a. 4.5 s b. 120 m c. 51 m/s 58 o below horizontal m m m Answers to are with each problem.