- #1

- 8

- 0

## Homework Statement

Particles of mud are thrown from the rim of a rolling wheel. If the forward speed of the

wheel is v

_{0}, and the radius of the wheel is b, show that the greatest height above the ground that the mud can go is

b + v

_{0}

^{2}/ 2g + gb

^{2}/ 2v

_{0}

^{2}

At what point on the rolling wheel does this mud leave?

(Note: It is necessary to assume that v

_{0}

^{2}≥bg.)

## Homework Equations

In 3 dimensions concept,

r = i b cosθ + j b sinθ

Since v = rω = rθ',

v = dr / dt = (-b sin θ i + b cos θ j) θ' = -v

_{0}( -sin θ i + cos θ j )

## The Attempt at a Solution

Firstly, find the time when the particle meets maximum height.

Take downwards as positive

for vertical direction,

v = u + at

0 = v

_{0}cos θ + g t

Then I find the time with minus sign.

It sounds quite weird.

In case, how do I know which side of rim the particle is thrown from rolling wheel?

The forum has already posted that problem already but still I have no idea with it.

Thanks.