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.
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
Transcribed Image Text: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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