Children playing in a playground on the flat roof of a city school lose their ball to the parking lot below. One of the teachers kicks the ball back up to the children as shown in the figure below. The playground is 4.70 m above the parking lot, and the school building's vertical wall ish- 6.10 m high, forming a 1.40 m high railing around the playground. The ball is launched at an angle of 53.0° above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) -d @ (a) Find the speed (in m/s) at which the ball was launched. x How is the horizontal distance the ball travels to the point above the wall related to the time of flight and initial velocity? m/s (b) Find the vertical distance (in m) by which the ball clears the wall. x What kinematics formula relates the final height to the time of flight, initial velocity, and acceleration? mi (c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands. x Can you find the time it takes the ball to travel to the final vertical height of the playground? Can you then relate this to the total horizontal distance the ball travels, and then the horizontal distance from the wall? m (d) What If? If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (Hint: You may need to use the trigonometric identity sec (0) = 1 + tan (0).) x What is the final x-position? The final y-position? How much time does it take the ball to travel to the final x-position in terms of the angle? Using this result in the equation for the final y-position, you should be able to write a quadratic equation for tangent of the angle. Be sure to use the trigonometric identity in the hint. above the horizontal (e) What would be the horizontal distance (in m) from the wall to the point on the roof where the ball lands in this case?

Children playing in a playground on the flat roof of a city school lose their ball to the parking lot below. One of the teachers kicks the ball back up to the children as shown in the figure below. The playground is 4.70 m above the parking lot, and the school building's vertical wall ish- 6.10 m high, forming a 1.40 m high railing around the playground. The ball is launched at an angle of 53.0° above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) -d @ (a) Find the speed (in m/s) at which the ball was launched. x How is the horizontal distance the ball travels to the point above the wall related to the time of flight and initial velocity? m/s (b) Find the vertical distance (in m) by which the ball clears the wall. x What kinematics formula relates the final height to the time of flight, initial velocity, and acceleration? mi (c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands. x Can you find the time it takes the ball to travel to the final vertical height of the playground? Can you then relate this to the total horizontal distance the ball travels, and then the horizontal distance from the wall? m (d) What If? If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (Hint: You may need to use the trigonometric identity sec (0) = 1 + tan (0).) x What is the final x-position? The final y-position? How much time does it take the ball to travel to the final x-position in terms of the angle? Using this result in the equation for the final y-position, you should be able to write a quadratic equation for tangent of the angle. Be sure to use the trigonometric identity in the hint. above the horizontal (e) What would be the horizontal distance (in m) from the wall to the point on the roof where the ball lands in this case?

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter3: Vectors And Two-Dimensional Motion

Section: Chapter Questions

Problem 70AP: A landscape architect is planning an artificial waterfall in a city park. Water flowing at 0.750 m/s...

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