How High Can a Pebble Flung from a Car Tire Reach?

[gmianosi]

Homework Statement

A car whose wheels are of radius r feet is driven at a speed v. A pebble is thrown from one of the wheels.
A. Neglecting air resistance, find the max height above the roadway which the pebble can reach as a function of r, g, and v.
B. For very small values of v, what does the height become?
C. For very large v, what angle gives the maximum height launch?

Homework Equations

velocity=ω*radius

The Attempt at a Solution

A. I would be able to solve this problem if I could get the velocity of the pebble when it's launched off of the wheel. I just don't know how to figure this out.

B. For small values of v, the height would just become the height from which it is released.

C. For large v, an angle of 0°would give it its max height launch (assuming the wheel is spinning counter clockwise).

 

[tiny-tim]

hi gmianosi!

A. I would be able to solve this problem if I could get the velocity of the pebble when it's launched off of the wheel. I just don't know how to figure this out.

the velocity will be the same as the velocity of the bit of the tyre that it comes from

vector-add the velocity of the centre of the wheel to the relative velocity of the tyre from the centre

B. For small values of v, the height would just become the height from which it is released.

yes, but so what is the greatest height (for any launch position)?

C. For large v, an angle of 0°would give it its max height launch (assuming the wheel is spinning counter clockwise).

why?

(and what difference does the spin direction make?)

 

[tms]

Deleted. I think tiny-tim's interpretation of the problem makes more sense than mine.