Question

A particle is moving along a curved path described by the equation r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j. Determine the velocity of the particle at a given value of θ.

Answer 1

Explanation:

the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

Answer 2

Explanation:

To find the velocity of the particle, we need to take the derivative of the position vector with respect to time.

r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j

d/dt[r(θ)] = d/dt[(a + b * cos(θ)) * i + (b * sin(θ)) * j]

d/dt[r(θ)] = (-b * sin(θ)) * i + (b * cos(θ)) * j

So, the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.