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Vector Calculus Help?
I have two questions.
1. A fighter plane which can only shoot bullets straight ahead travels along the path
r(t) = < 5 - t, 21 - (t^2), 3 - (t^3)/27>
Show that there is precisely one time t at which the pilot can hit a target located at the origin.
2. Use the parameterization r = <rcosθ, rsinθ> to show that a curve r in polar coordinates has curvature:
r(θ) = | (r^2) + 2(r')^2 - r(r'')| / [( (r^2) + (r')^2 )^(3/2)]
1 Answer
- ted sLv 71 decade agoFavorite Answer
1 . dr /dt = < - 1 , - 2t , - 3 t² > / 27 = zero vector never
2. straight forward with algebra...need | x ' y ' ' - y ' x ' ' | / [ ( x' )² + ( y ' )²]^(3/2)
dx / dΘ = r ' cos Θ - r sin Θ , d²x / dΘ² = r ' ' cos Θ - 2 r ' sin Θ - r cos Θ
dy / dΘ = r ' sin Θ + r cos Θ, d²y / dΘ² = r ' ' sin Θ + 2 r ' cos Θ - r sin Θ
do the work !!
