Aaron was challenged to kick a soccer ball off of the flat roof of the Science Building and into a trashcan 12.3 m away from the edge of the building. The Science Building is 11.3 m tall. Since this is unsafe, Aaron suggested that he works it out on paper instead. Assuming the ball is kicked off the building with only a horizontal velocity, how fast would the ball need to leave the top of the building to land in the trash can?

Question

Physics

Justice

25 May, 18:11

Aaron was challenged to kick a soccer ball off of the flat roof of the Science Building and into a trashcan 12.3 m away from the edge of the building. The Science Building is 11.3 m tall. Since this is unsafe, Aaron suggested that he works it out on paper instead. Assuming the ball is kicked off the building with only a horizontal velocity, how fast would the ball need to leave the top of the building to land in the trash can?

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Answers (1)

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Mcdonald · Answer 1

8.1 m / s

Explanation:

Let the required velocity be v. This is a horizontal velocity so it will cover the horizontal distance of 12.3 m with this velocity without any acceleration.

Time taken t = distance / velocity

t = 12.3 / v

During this period ball also covers vertical distance with initial velocity zero and acceleration of g.

For vertical fall

initial velocity u = 0

Acceleration = g

Time = t

h = ut + 1/2 g t²

11.3 = 0 +.5 x 9.8 x (12.3 / v) ²

v² = 65.6

v = 8.1 m / s