Question

In: Physics

Children playing in a playground on the flat roof of a city school lose their ball...

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 4.80 m above the parking lot, and the school building's vertical wall is h = 6.30 m high, forming a 1.50 m high railing around the playground. The ball is launched at an angle of θ = 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.) A man on the ground kicking a ball to children on a flat rooftop is shown. The distance between the man and the building is labeled d. The height of the building is labeled h. The motion of the ball is depicted as a parabola originating from the man on the ground and ending at the rooftop. The vector of the initial motion of the ball makes an angle θ with the horizontal. (a) Find the speed (in m/s) at which the ball was launched. 18.12698 Correct: Your answer is correct. m/s (b) Find the vertical distance (in m) by which the ball clears the wall. 1.833 Correct: Your answer is correct. m (c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands. 4.06 Correct: Your answer is correct. 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(θ) = 1 + tan2(θ).) 37.45 Incorrect: Your answer is incorrect. 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?

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Expert Solution

Here we apply concept of kinematics and apply equation of motion in two dimension separately.

genius_generous answered 2 hours ago
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