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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 straight-line 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 free-fall 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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