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Solution #2 summer2007

# Solution #2 summer2007 - Physics 2211 A Quiz#2 Solutions...

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Unformatted text preview: Physics 2211 A Quiz #2 Solutions Summer 2007 g Earth = 9 . 8m / s 2 Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected. I . (16 points) Sand moves without slipping at a speed v = 4 . 0m / s up a conveyer that is tilted at an angle θ = 25 ◦ , as illustrated. The sand enters a pipe a height h = 2 . 5m below the end of the conveyer belt. What is the horizontal distance d between the conveyer belt and the pipe? (On Earth.) . . . . . . . . . . . . . . . . . . . . . . . This is a projectile motion problem. That is, it is a two-dimensional constant acceleration problem, in which the horizontal acceleration is zero, and the vertical acceleration is the acceleration of gravity. First, choose a coordinate system. In the illustration, the posi- tive directions are upward and rightward, and the sand leaves the conveyer at x = 0 and enters the pipe at y = 0. The time required for the sand to fall can be determined from the vertical information: y = y + v y Δ t + 1 2 a y (Δ t ) 2 ⇒ 1 2 a y (Δ t ) 2 + v y Δ t + ( y- y ) = 0 This is a quadratic in Δ t , so Δ t =- B ± √ B 2- 4 AC 2 A where A = 1 2 a y = 1 2 (- 9 . 8m / s 2 ) =- 4 . 9m / s 2 B = v y = v sin θ = (4 . 0m / s)sin25 ◦ = 1 . 69m / s C = ( y- y ) = 2 . 5m- 0m = 2 . 5m This yields two times, -0.56s or 0.91s. Choose the positive time, 0.91s, as the sand must enter the pipe after it leaves the conveyer. With this time, the horizontal distance travelled can be determined from the horizontal information: x = x + v x Δ t + 1 2 a x (Δ t ) 2 ⇓ d = 0m + v cos θ Δ t + 1 2 ( 0m / s 2 ) (Δ t ) 2 = (4 . 0m / s)cos25 ◦ (0 . 91s) = 3 . 3m Quiz #2 Solutions Page 1 of 5 II . (16 points) Current flows from right to left at 2.0m/s in the illustrated river. The boat is capable of moving at 5.0m/s in still water. The river is 200m wide, and the captain wants to land at a point on the opposite shore and 50m upstream from his starting point. At what angle, φ , from straight across should the bow of the boat be directed? Hint: You may want to find the angle θ at which the captain wants to travel, first, and then find an angle that represents the difference between θ and φ ....
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Solution #2 summer2007 - Physics 2211 A Quiz#2 Solutions...

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