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M2 Help Needed

r=2cos⁡(t)i+2sin⁡(t)j+(10−.4t)kr = 2\cos (t) i + 2\sin (t) j + (10-.4t)k

The perpendicular unit vectors i and j are in the horizontal plane and the unit vector k is directed vertically upwards.

Write down the first two values of t for which Tom is directly below his starting
point.

Here is what I did:
The i and j components must be 0, so

2cos⁡(t)=02\cos (t) = 0
t=π2,3π2,5π2,7π2.........t = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2} .........

2sin⁡(t)=02\sin (t) = 0
t=0,π,2π,3π,4π.........t = 0, \pi, 2\pi, 3\pi, 4\pi .........

Now I cant get a value of t in which both are 0, let alone a value for which bot are 0 and the K component is negative.

Help is highly appreciated :smile:

Edit: The MS says that the answers are t = 2pi and t= 4 pi. But putting t=2pi in gives r = 2i + 3.7k, which can't be directly below his starting position as it has moved 2 units east and 3.7 units up ?? And the same problem occurs when t=4 is put in.
(edited 12 years ago)
Reply 1
Avatar for a.partridge
a.partridge
hint: when t = 0

i = 2
j = 0

:smile:
Reply 2
Avatar for member910132
member910132
OP
Original post by a.partridge
hint: when t = 0

i = 2
j = 0

:smile:


But I need i = 0, j = 0 and k to be negative.
Reply 3
Avatar for a.partridge
a.partridge
Original post by member910132
But I need i = 0, j = 0 and k to be negative.


well no value exists where cos(t) and sin(t) are both 0

but that doesn't matter because at the starting point (i) and (j) are not both 0.

the starting point comes from r(0) = ........ you see :smile: not the origin!
Reply 4
Avatar for a.partridge
a.partridge
regarding the negative you can see that the solutions must be the first to satisfy the inequality

(A)t > 10 there A is the coefficient in the expression for the displacement parallel to K
Reply 5
Avatar for member910132
member910132
OP
Original post by a.partridge
well no value exists where cos(t) and sin(t) are both 0

but that doesn't matter because at the starting point (i) and (j) are not both 0.

the starting point comes from r(0) = ........ you see :smile: not the origin!


Thnx a lot for that :smile::smile:

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