   Chapter 12.1, Problem 88E

Chapter
Section
Textbook Problem

# Particle MotionIn Exercises 89 and 90, two particles travel along the space curves r ( t ) and u ( t ) . Do the particles collide? Do their paths intersect? r ( t ) = t i + t 2 j + t 3   k u ( t ) = ( − 2 t + 3 ) i + 8 t j + ( 12 t + 2 ) k

To determine
If two particles having space curves r(t) and u(t). They will collide and whether their paths will intersect.

Explanation

Consider the particle travel along space curve r(t)=ti+t2j+t3k and u(s)=(2s+3)i+8sj+(12s+2)k.

Now if the particles collide then at that value of t all the equations will be satisfied.

So, equate the components;

t=2s+3 …...…... (1)

t2=8s …...…... (2)

t3=12s+2 …...…... (3)

Use equation (1) and (2), to get;

(2s+3)2=8s4s212s+9=8s4s220s+9=0(2s9)(2s1)=0

Simplify the above equation,

s=12 and s=92

From equation (1),

t

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