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# oldhw 07 - alexander(jra2623 oldhomework 07 Turner(92510...

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alexander (jra2623) – oldhomework 07 – Turner – (92510) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points You are standing at the top of a cliff that has a stairstep configuration. There is a vertical drop of 6 m at your feet, then a horizontal shelf of 10 m , then another drop of 4 m to the bottom of the canyon, which has a horizontal floor. You kick a 0 . 31 kg rock, giving it an initial horizontal velocity that barely clears the shelf below. 10 m Δ x 10 m v 6 m 4 m What initial horizontal velocity v will be required to barely clear the edge of the shelf below you? The acceleration of gravity is 9 . 8 m / s 2 . Consider air friction to be negligi- ble. Correct answer: 9 . 03696 m / s. Explanation: Let : y 1 = 6 m , y 2 = 4 m , and x = 10 m . Since all of the vertical motion is down, we can consider down to be positive, and deal with positive gravity, vertical velocities, and distances. Thus v oy = 0, and vertical distances are defined by y = 1 2 g t 2 There is an initial horizontal velocity but a ox = 0, so horizontal distances are defined by x = v ox t Once launched, the vertical motion defines the time to drop to the first shelf 2 y 1 = g t 2 1 so t 1 = radicalbigg 2 y 1 g Thus the horizontal distance traveled is x = v ox t 1 so v ox = x t 1 = x radicalbigg g 2 y 1 = (10 m) radicalBigg (9 . 8 m / s 2 ) 2 (6 m) = 9 . 03696 m / s . 002 (part 2 of 2) 10.0 points How far from the bottom of the second cliff will the projectile land? Correct answer: 2 . 90994 m. Explanation: The time to drop the distance y = y 1 + y 2 to the bottom of the cliff is t = radicalBigg 2 [ y 1 + y 2 ] g , and the total horizontal distance traveled in that time is x 2 = v ox t = v ox radicalBigg 2 [ y 1 + y 2 ] g = (9 . 03696 m / s) radicalBigg 2 [(6 m) + (4 m)] 9 . 8 m / s 2 = 12 . 9099 m . Thus the projectile will land a distance Δ x = x 2 - x = (12 . 9099 m) - (10 m) = 2 . 90994 m ,

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alexander (jra2623) – oldhomework 07 – Turner – (92510) 2 from the bottom of the cliff.
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oldhw 07 - alexander(jra2623 oldhomework 07 Turner(92510...

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