HW7 - Pickering Tracey – Homework 7 – Due Feb 6 2006...

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Unformatted text preview: Pickering, Tracey – Homework 7 – Due: Feb 6 2006, noon – Inst: Drummond 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A 2 . 20 m tall basketball player attempts a goal 13 . 00 m from the basket (3 . 05 m high). The acceleration of gravity is 9 . 81 m / s 2 . 2 . 2 m 3 . 05 m 13 m v 41 ◦ If he shoots the ball at a 41 . ◦ angle, at what initial speed must he throw the basket- ball so that it goes through the hoop without striking the backboard? Correct answer: 11 . 8008 m / s. Explanation: 2 . 2m 3 . 05m 13 m Note: Figure is not drawn to scale Basic Concepts: Horizontally, Δ x = v i (cos θ ) Δ t Vertically, Δ y = v i (sin θ ) Δ t- 1 2 g (Δ t ) 2 Given: Δ x = 13 . 00 m θ = 41 . ◦ Δ y = 3 . 05 m- 2 . 20 m = 0 . 850 m g = 9 . 81 m / s 2 Solution: From the horizontal motion, Δ t = Δ x v i (cos θ ) so that Δ y = v i (sin θ ) • Δ x v i (cos θ ) ‚- 1 2 g • Δ x v i (cos θ ) ‚ 2 = Δ x (tan θ )- g (Δ x ) 2 2 v 2 i (cos θ ) 2 g (Δ x ) 2 2 v 2 i (cos θ ) 2 = Δ x (tan θ )- Δ y where Δ x (tan θ )- Δ y = (13 m) (tan 41 ◦ )- . 85 m = 10 . 4507 m so that v i = s g (Δ x ) 2 2 (cos θ ) 2 [Δ x (tan θ )- Δ y ] = s (9 . 81 m / s 2 ) (13 m) 2 2 (cos 41 ◦ ) 2 (10 . 4507 m) = 11 . 8008 m / s 002 (part 1 of 2) 10 points A person can jump a horizontal distance of 1 . 6 m on Earth. a) How far could the person jump on the moon, where the free-fall acceleration is g/ 6 and g = 9 . 81 m / s 2 ? Correct answer: 9 . 6 m. Explanation: Basic Concepts: Horizontally, Δ x = v i (cos θ )Δ t Pickering, Tracey – Homework 7 – Due: Feb 6 2006, noon – Inst: Drummond 2 Vertically, Δ y = v i (sin θ )Δ t- 1 2 g (Δ t ) 2 = 0 Given: Δ x Earth = 1 . 6 m g Earth = 9 . 81 m / s 2 g moon = g Earth 6 m / s 2 Solution: From the vertical motion, v i (sin θ ) = 1 2 g Δ t Δ t = 2 v i (sin θ ) g Thus Δ x Earth = v i (cos θ ) • 2 v i (sin...
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HW7 - Pickering Tracey – Homework 7 – Due Feb 6 2006...

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