Derivative of position question

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The discussion revolves around determining the time at which a dragonfly's velocity vector makes a 30-degree angle clockwise from the x-axis, based on its position function. The user correctly identifies the need to take the derivative of the position vector to find the velocity. After calculating the velocity, they attempt to use the tangent function to relate the components and solve for time, initially arriving at t = 69.28. However, they later acknowledge making a careless mistake in their calculations. The conversation highlights the importance of careful evaluation in solving physics problems.
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Homework Statement



Q:
The position of a dragonfly that is flying parallel to the ground is given as a function of time by r⃗ =[2.90m+(0.0900m/s2)t^2]i^− (0.0150m/s3)t^3j^ .

At what value of t does the velocity vector of the insect make an angle of 30.0 ∘ clockwise from the x-axis?
.

Homework Equations


none

The Attempt at a Solution


What I did so far: Well I'm pretty sure the first step is to take the derivative of the position vector. I did that and got (0.18t)i^2-(0.045t^2)j^2.

I tried to use tan30=0.18t/0.048t^2 and solve for t

I get t=69.28 but I'm not sure if that is 100% correct
 
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Check this part of the question:

At what value of t does the velocity vector of the insect make an angle of 30.0 ∘ clockwise from the x-axis?

What can you defer from this?

Also,
I believe your evaluation of "t" has some mistakes.
 
never mind I got it

was trying to do it too fast and ended up making a careless mistake

thanks
 
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