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Ratling [72]
3 years ago
13

Suppose that a particle following the given path c(t) flies off on a tangent at t = t0. Compute the position of the particle at

the given time t1. c(t) = (2t2, t3 − 4t, 0), where t0 = 3, t1 = 4
Mathematics
1 answer:
Svetach [21]3 years ago
4 0

Answer:

(30,35,0)

Step-by-step explanation:

We are given that

C(t)=(2t^2,t^3-4t,0)

t_0=3,t_1=4

The velocity of particle,v(t)=c'(t)=(4t,3t^2-4,0)

Substitute t_0=3

C(3)=(2(3)^2,(3)^3-4(3),0))=(18,15,0)

v(3)=(4(3),3(3)^2-4,0)=(12,23,0)

The tangent line at t=3 is given by

l(t)=c(2)+(t-3)v(3)=(18,15,0)+(t-3)(12,23,0)

Now, substitute t=4

l(4)=(18,15,0)+(4-3)+(12,23,0)=(18,12,0)+(12,23,0)

l(4)=(30,35,0)

Hence, the position of particle  at t_1=4=(30,35,0)

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