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 4.60 m above the parking lot, and the school building's vertical wall is h= 6.10 m high, forming a 1.50 m high railing around the playground. The ball is launched at an angle of 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 do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) 53.0 (Due to the nature of this problem, wall. mwi

Elements Of Electromagnetics
7th Edition
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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 4.60 m above the parking lot, and the school building's vertical wall is h= 6.10 m high, forming a 1.50 m high railing around the playground. The
ball is launched at an angle of 0 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.)
UN
BUNT
Transcribed Image Text: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 4.60 m above the parking lot, and the school building's vertical wall is h= 6.10 m high, forming a 1.50 m high railing around the playground. The ball is launched at an angle of 0 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.) UN BUNT
(a) Find the speed (in m/s) at which the ball was launched.
16.13
✓mys
(b) Find the vertical distance (in m) by which the ball clears the wall.
2.03
✓ m
(c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands.
13.1
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 sec²(0) - 1+ tan²(0).)
45
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?
m
Transcribed Image Text:(a) Find the speed (in m/s) at which the ball was launched. 16.13 ✓mys (b) Find the vertical distance (in m) by which the ball clears the wall. 2.03 ✓ m (c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands. 13.1 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 sec²(0) - 1+ tan²(0).) 45 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? m
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