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Q24.

Expert-verified
Geometry
Found in: Page 581
Geometry

Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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Short Answer

A rolling ball that does not have much spin will bounce off a wall so that the two angles that the path forms with the wall are congruent. Thus, to roll the ball from B off the wall shown and into hole H, you need to aim the ball so that 12.

  1. Let H' be the image of H by reflection in the wall. BH' Intersects the wall at P. Why is 13? Why is 32? Why is 12? You can conclude that if you aim for H', the ball will roll to H.
  2. Show that the distance travelled by the ball equals the distance H.

  1. 12,13and32.
  2. The distance travelled by the ball equals the distance BH'.
See the step by step solution

Step by Step Solution

a.Step 1. Given Information.

H' Is the image of H by reflection in the wall and BH'¯ intersects the wall at P.

Step 2. Proof.

13 vertically opposite angles

In triangles PXH and PXH'.

PX=PX common sidemX=mX each equals to 90°HX=HX' perpendicular bisector

By side angle side congruency

ΔPXHΔPXH'23

Since 13 and 23 therefore 12

Step 3. Conclusion.

Hence, the congruency of angles is proved.

b.Step 1. Given Information.

H' Is the image of H by reflection in the wall and BH'¯ intersects the wall at P.

Step 2. Proof.

ΔPXHΔPXH'PH=PH'

Distance travelled by the ball is,

BP+PH=BP+PH'=BH'

Step 3. Conclusion.

Hence, it is proved that the distance travelled by the ball equals the distance BH'.

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