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) t2]i^ - (0.0150m/s3) t3j^.

At what value of t does the velocity vector of the insect make an angle of 36.0 ∘ clockwise from the x-axis? ... t=?

Question

Shaun Figueroa

Physics

16 November, 06:42

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) t2]i^ - (0.0150m/s3) t3j^.

At what value of t does the velocity vector of the insect make an angle of 36.0 ∘ clockwise from the x-axis? ... t=?

+4

Answers (1)

Know the Answer?

Tyree Simon · Answer 1

The solution for this problem is:

r = [ (2.90 + 0.0900t²) i - 0.0150t³ j] m/s²

this is for t in seconds and r in meters

v = dr/dt = [0.180t i - 0.0450t² j] m/s²

tan (-36.0º) = - 0.0450t² / 0.180t

0.7265 = 0.25t

t = 2.91 s is the velocity vector of the insect

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) t2]i^ - (0.0150m/s3) t3j^.At what value of t does the velocity vector of the insect make an angle of 36.0 ∘ clockwise from the x-axis? ... t=?

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) t2]i^ - (0.0150m/s3) t3j^.

At what value of t does the velocity vector of the insect make an angle of 36.0 ∘ clockwise from the x-axis? ... t=?