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 2 years 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.
 2 years 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.

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Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1first, 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?

Lcoohill
 2 years ago
Best ResponseYou've already chosen the best response.0yes 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 ??

Lcoohill
 2 years ago
Best ResponseYou've already chosen the best response.0vb  va = 0i  vvj ??

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

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1\(r_B(0)−r_A(0)=C=−9i+6j\)

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

Lcoohill
 2 years ago
Best ResponseYou've already chosen the best response.0kind 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

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

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

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1and for the third question, you'll have to find the minimum value of rBA.

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

Lcoohill
 2 years ago
Best ResponseYou've already chosen the best response.0thank you very much , you were great help and i understand it so much better !!
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