Show that the vectors a = 3i+ 4j and b = 4i - 3j are perpendicular. A smooth sphere A of mass 2m moving on a smooth horizontal floor with velocity (10i +5j)ms" impinges obliquely on a smooth stationary sphere B of mass m. At the instant of collision the line joining the centres of the spheres is parallel to the vectora. Given that the coefficient of restitution between the two spheres is e and that the direction of motion of sphere A afterimpact makes an angle a with the line of centres of the spheres, show that (a) (4-2e) tan a = 3, 3 (b) s tan a s- 2 (c) Given that tan a s1, find e and hence find the velocitics of A andB after impact.

Show that the vectors a = 3i+ 4j and b = 4i - 3j are perpendicular. A smooth sphere A of mass 2m moving on a smooth horizontal floor with velocity (10i +5j)ms" impinges obliquely on a smooth stationary sphere B of mass m. At the instant of collision the line joining the centres of the spheres is parallel to the vectora. Given that the coefficient of restitution between the two spheres is e and that the direction of motion of sphere A afterimpact makes an angle a with the line of centres of the spheres, show that (a) (4-2e) tan a = 3, 3 (b) s tan a s- 2 (c) Given that tan a s1, find e and hence find the velocitics of A andB after impact.

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Description: Show all working explaining detailly each stepAnswer must be typewritten with a computer keyboard!Answer Q3a, b, & c 3. Show that the vectors a = 3i+ 4j and b = 4i- 3j are perpendicular. A smooth sphere A of mass2m moving on a smooth horizontal floor

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Answer Q3a, b, & c

3. Show that the vectors a = 3i+ 4j and b = 4i- 3j are perpendicular. A smooth sphere A of mass
2m moving on a smooth horizontal floor with velocity (10i +5j)ms impinges obliquely on a
smooth stationary sphere B of mass m. At the instant of collision the line joining the centres of the
spheres is parallel to the vectora. Given that the coefficient of restitution between the two spheres
is e and that the direction of motion of sphere A after impact makes an angle a with the line of
centres of the spheres, show that
(a) (4 - 2e) tan a = 3,
.3
3
(b) s tan a s
2
evi
(c) Given that tan a s1, find e and hence find the velocities of A andB after impact.

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