1. A particle is moving along the curve below.

y = 2sin(πx/2)

As the particle passes through the point (1/3,1) its x-coordinate increases at a rate of sqrt(10) cm/s. How fast is the distance from the particle to the origin changing at this instant?

Question

1. A particle is moving along the curve below.

y = 2sin(πx/2)

As the particle passes through the point (1/3,1) its x-coordinate increases at a rate of sqrt(10) cm/s. How fast is the distance from the particle to the origin changing at this instant?

amistre64 · Answer

r^2 = x^2+y^2

amistre64 · Answer

x'=sqrt(10)

2r r' = 2x x' + 2y y'

r' = (2x x' + 2y y')/2r

r' = (x x' + y y')/r

we know x'; amd since y is a function of x we can know y' as well

amistre64 · Answer

y = 2sin(πx/2)

y' = pi cos(x pi/2)