Uniform Circualr Motion with Projectile Motion problem (Extremely confusing):

[VinnyCee]

A lump of wet putty moves in uniform circular motion of radius 20cm on the rim of a wheel rotating counter clockwise with a period of 5.00 seconds. The lump fly's off the rim at the 5 o'clock position and from a height of 1.20m above the ground and a distance of 2.50m from a wall. At what height on the wall does the lump hit?

I have been stumped by this problem for hours. Please help.

 

[robphy]

step 1: What is the position and the velocity vector of the lump as it leaves the wheel?

 

[VinnyCee]

Position is at 60 degrees below the positive x-axis with a velocity of .25 m / ms or 250 m / s, right?

 

[VinnyCee]

I guess the answer is supposed to be 2.64 meters height on the wall that is 2.50 meters away.

But I really need to know how to actually DO the problem!

Please help:)

 

[robphy]

For your projectile, the initial Position Vector (when it leaves the wheel) has an x-component (call it x₀) and a y-component (call it y₀). (Use your "60 degrees below the positive x-axis" and the wheel radius to determine these components).

The initial Velocity Vector also has an x-component (call it v_0,x) and a y-component (call it v_0,y). To get these components, first determine its magnitude (the speed) by considering how fast a point on the wheel's rim is traveling... (in one full rotation of wheel, what distance was traveled by a point on the rim in one period of 5 s?). Then determine the direction (the angle of launch) by arguing that the initial velocity vector is tangent to the wheel when it leaves the wheel.

You now have your initial conditions for the projectile.

Now, where is the wall and the floor in relation to your starting position?
At least one of those will determine your final position.

Write down your projectile equations and see what is given and what is unknown.
Formulate an strategy to algebraically solve for your unknowns.