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phy3 - homework 03 JACOBS AMBER Due Feb 5 2008 1:00 am...

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homework 03 – JACOBS, AMBER – 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 . 1 kg shell with initial velocity v i = 9 . 7 m / s in the direction θ = 47 above the horizontal. The acceleration of gravity is 9 . 8 m / s 2 . Δ x Δ h 9 . 7 m / s 47 Δ y y Shell’s trajectory curves downward because of gravity, so at the time t = 0 . 782 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: 2 . 99647 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 . 782 s) 2 2 = 2 . 99647 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. The ball is in free-fall and there is no acceleration at any point on its path. 2. correct 3.
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homework 03 – JACOBS, AMBER – Due: Feb 5 2008, 1:00 am 2 4. 5. 6. 7. 8. 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 . 3 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 17 m / s at angle of 50 above the horizontal. The top of the fence is 7 m high. The kicker’s foot is in contact with the ball for 0 . 03 s. The ball hits nothing while in flight and air resistance is negligible. The acceleration due to gravity is 9 . 8 m / s 2 . 20 m 7 m 17 m / s 50 Determine the magnitude of the average net force exerted on the ball during the kick. Correct answer: 170 N (tolerance ± 1 %). Explanation: Let : m = 0 . 3 kg , θ = 50 , v 0 = 17 m / s , and Δ t = 0 . 03 s . From Newton’s second law, F avg = m a avg . With a avg = Δ v Δ t , F avg = m a avg = m Δ v Δ t = m v 0 Δ t = (0 . 3 kg) parenleftbigg 17 m / s 0 . 03 s parenrightbigg = 170 N .
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