oldhw8_s - oldhomewk 08 – YOO HEE – Due Feb 5 2008 4:00...

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Unformatted text preview: oldhomewk 08 – YOO, HEE – Due: Feb 5 2008, 4:00 am 1 Question 1, chap 4, sect 4. part 1 of 2 10 points Janet jumps off a high diving platform with a horizontal velocity of 2 . 39 m / s and lands in the water 3 s later. The acceleration of gravity is 9 . 8 m / s 2 . a) How high is the platform? Correct answer: 44 . 1 m (tolerance ± 1 %). Explanation: Basic Concepts: Horizontally, v oh = v cos θ v h = v oh d = v oh t Vertically, all the motion is directed down- ward, so down can be considered positive, and v ov = v sin θ v v = v ov + g t h = v ov t + 1 2 g t 2 . Solution: The height of the fall is h = v o t + 1 2 g t 2 = 1 2 g t 2 . Question 2, chap 4, sect 4. part 2 of 2 10 points b) How far from the base of the platform does she land? Correct answer: 7 . 17 m (tolerance ± 1 %). Explanation: The horizontal velocity is constant, so the horizontal distance is d = v t . Question 3, chap 4, sect 5. part 1 of 5 10 points A flea is at point A on a horizontal turntable 10 cm from the center. Place the coordinate origin at the center of the turntable with the positive x axis fixed in space and initially passing through A . The turntable is rotating at 31 rev / min in the counterclockwise direction relative to the fixed coordinate system. Then the flea jumps upward (meaning that it adds only to its own vertical velocity when it jumps, not to its horizontal velocity) to a height of 6 . 5 cm in the fixed coordinate system and lands on the turntable at point B . The acceleration of gravity is 9 . 8 m / s 2 . Find the linear displacement of the flea in the fixed coordinate system. Correct answer: 0 . 0747789 m (tolerance ± 1 %). Explanation: Note: vextendsingle vextendsingle A B vextendsingle vextendsingle = vextendsingle vextendsingle A A ′ vextendsingle vextendsingle y = v A t = R A ω t x y A B A ′ θ A θ B y = v A t The angular frequency of the turntable is given by ω = (31 rev / min) 2 π rad rev 1 min 60 s = 3 . 24631 rad / s . Therefore, the speed at point A is v A = ω r A = (3 . 24631 rad / s) (0 . 1 m) = 0 . 324631 m / s . We note that, since point A coincides initially with the x axis, and the turntable is rotating counterclockwise, the velocity at point A is vectorv A = (0 . 324631 m / s) vector. oldhomewk 08 – YOO, HEE – Due: Feb 5 2008, 4:00 am 2 This is the y component of the velocity of the flea as it jumps vertically up. Now we need to get the time to jump to a height of 0 . 065 m and to land. Note: According to our axes, the vertical direction is along the z axis, and...
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This note was uploaded on 05/04/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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oldhw8_s - oldhomewk 08 – YOO HEE – Due Feb 5 2008 4:00...

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