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Two particles A and B have velocities 3i and vj respectively (in m/s).
(a) Find rBA, the position of B relative to A for all t given that rBA(t = 0) = −9i+6j
(in meters).
(b) Find the value of v such that A and B collide.
(c) If v = 1 m/s, ﬁnd the time and distance when A and B are closest together.
 one year ago
 one year ago
Two particles A and B have velocities 3i and vj respectively (in m/s). (a) Find rBA, the position of B relative to A for all t given that rBA(t = 0) = −9i+6j (in meters). (b) Find the value of v such that A and B collide. (c) If v = 1 m/s, ﬁnd the time and distance when A and B are closest together.
 one year ago
 one year ago

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ShadowysBest ResponseYou've already chosen the best response.1
first, you need to find \(r_B(t)\) and \(r_A(t)\) through integration and then, since they are vectors,dw:1354622967278:dw \(r_B(t)r_A(t)\) is the relative distance. You follow?
 one year ago

LcoohillBest ResponseYou've already chosen the best response.0
yes i get that alright i know you integrate 9i+6j to 9ti+6tj ?? not sure exactly . do i integrate A and B ? bit confused with the vj ??
 one year ago

LcoohillBest ResponseYou've already chosen the best response.0
vb  va = 0i  vvj ??
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
you integrate \(v_A(t)=3i\) to get \(r_A(t)=3ti+C_A\) and \(v_B(t)=vj\) to get \(r_B(t)=vtj+C_B\) \(r_B(t)r_A(t)=vtj+C_B3tiC_A=vtj3ti+C\)
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
\(r_B(0)−r_A(0)=C=−9i+6j\)
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
so, \(r_B(t)−r_A(t)=3(t+3) i + (vt+6) j\) :) you follow? you'll have to do them one by one
 one year ago

LcoohillBest ResponseYou've already chosen the best response.0
kind of sorry was thought different way in college and am just really confused i get what u are saying to integrate both to get position and then take a from b
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
ah. perhaps my solution was a little...um, confusing. :) so you've got rBA? for the second question, \(r_A(t)=r_B(t)\)
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
because they collide.
 one year ago

LcoohillBest ResponseYou've already chosen the best response.0
yes i get the first piece , and for part b you let them equal each other because they collide
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
and for the third question, you'll have to find the minimum value of rBA.
 one year ago

LcoohillBest ResponseYou've already chosen the best response.0
yes a and b are closest together when d = 3(t+3)i+(vt+6)j is minimized eg D'=0 ???
 one year ago

LcoohillBest ResponseYou've already chosen the best response.0
thank you very much , you were great help and i understand it so much better !!
 one year ago
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