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Unformatted text preview: homework 03 – ALLEN, HUNTER – Due: Feb 5 2008, 1:00 am 1 Question 1, chap 4, sect 5. part 1 of 1 10 points A toy cannon fires a 0 . 08 kg shell with initial velocity v i = 12 m / s in the direction θ = 58 ◦ above the horizontal. The acceleration of gravity is 9 . 8 m / s 2 . Δ x Δ h 1 2 m / s 5 8 ◦ Δ y y Shell’s trajectory curves downward because of gravity, so at the time t = 0 . 783 s the shell is below the straight line by some vertical distance. Your task is to calculate this distance Δ h in the absence of air resistance. Correct answer: 3 . 00414 m (tolerance ± 1 %). Explanation: In the absence of gravity, the shell would fly along the straight line at constant velocity: ˆ x = t v i cos θ , ˆ y = t v i sin θ . The gravity does not affect the x coordinate of the shell, but it does pull its y coordinate at constant downward acceleration a y = − g , hence x = t v i cos θ, y = t v i sin θ − g t 2 2 . Thus, x = ˆ x but y = ˆ y − 1 2 gt 2 , or in other words, the shell deviates from the straightline path by the vertical distance Δ h =  ˆ y − y  = g t 2 2 . Note: This result is completely indepen dent on the initial velocity v i or angle θ of the shell. It is a simple function of the flight time t and nothing else (besides the constant g = 9 . 8 m / s 2 ). Δ h = g t 2 2 = (9 . 8 m / s 2 ) (0 . 783 s) 2 2 = 3 . 00414 m . Question 2, chap 4, sect 5. part 1 of 1 10 points A ball is thrown and follows the parabolic path shown. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground. Q R P Which of the following diagrams best indi cates the direction of the acceleration, if any, on the ball at point R ? 1. 2. 3. homework 03 – ALLEN, HUNTER – Due: Feb 5 2008, 1:00 am 2 4. 5. correct 6. 7. 8. The ball is in freefall and there is no acceleration at any point on its path. 9. Explanation: Since air friction is negligible, the only ac celeration on the ball after being thrown is that due to gravity, which acts straight down. Question 3, chap 4, sect 5. part 1 of 4 10 points A ball of mass 0 . 4 kg, initially at rest, is kicked directly toward a fence from a point 20 m away, as shown below. The velocity of the ball as it leaves the kicker’s foot is 19 m / s at angle of 63 ◦ above the horizontal. The top of the fence is 12 m high. The kicker’s foot is in contact with the ball for 0 . 05 s. The ball hits nothing while in flight and air resistance is negligible. The acceleration due to gravity is 9 . 8 m / s 2 . b 20 m 12 m 1 9 m / s 6 3 ◦ b b b b b b b b b b b b b b b b b b b b Determine the magnitude of the average net force exerted on the ball during the kick....
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This note was uploaded on 04/06/2008 for the course PHY 317k taught by Professor Kopp during the Spring '07 term at University of Texas.
 Spring '07
 KOPP
 Physics, Work

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