Trajectory of Mud Glob Thrown From Wheel: Solving the Mystery

[physicsnoob1]

Homework Statement

A wheel of radius r is rolling along a muddy road with speed v, and particles of mud are being continuously thrown off from all points of the wheel. ignoring air resistance, what is the trajectory of a mud glob thrown off the wheel when it is at angle (theta) to the horizontal? at what (theta) is the height maximized? What is the meaning of the critical speed v^2 = rg?

Homework Equations

v = 2(pi)r / T is the propagation velocity of the wheel. but my first question is, is this the same as the rotational velocity? I've thought about it for a while and it seems like it is. i am stumped as to how to find the trajectory of the mud glob though. please help!

The Attempt at a Solution

well i guess I am still stuck on figuring out if the propagation velocity is the same as the rotational velocity. after that i was thinking about playing with the velocity vectors to find an expression for the trajectory. the only force acting on the glob should be gravity i think.

 

[Hootenanny]

Welcome to Physics Forums.

Have you tried to sketch the problem? You know that when the wheel is at some angle, theta, a mud particle flies off. In what direction relative to the wheel will the particle travel?

 

[Richyfeller]

Homework Statement

A wheel of radius r is rolling along a muddy road with speed v, and particles of mud are being continuously thrown off from all points of the wheel. ignoring air resistance, what is the trajectory of a mud glob thrown off the wheel when it is at angle (theta) to the horizontal? at what (theta) is the height maximized? What is the meaning of the critical speed v^2 = rg?

Homework Equations

v = 2(pi)r / T is the propagation velocity of the wheel. but my first question is, is this the same as the rotational velocity? I've thought about it for a while and it seems like it is. i am stumped as to how to find the trajectory of the mud glob though. please help!

The Attempt at a Solution

well i guess I am still stuck on figuring out if the propagation velocity is the same as the rotational velocity. after that i was thinking about playing with the velocity vectors to find an expression for the trajectory. the only force acting on the glob should be gravity i think.

Please help me to show that, if v^2=gr, no mud can be thrown higher than r+v^2/2g+gr^2/2v^2 above the ground,

 

[Richyfeller]

Please help me to show that, if v^2=gr, no mud can be thrown higher than r+v^2/2g+gr^2/2v^2 above the ground,

Welcome to Physics Forums.

Have you tried to sketch the problem? You know that when the wheel is at some angle, theta, a mud particle flies off. In what direction relative to the wheel will the particle travel?

yes i sketch the problem, but the equations to use for the proof is my problem