# How much ahead the front axle does the wheel jet the water that it pick

1. Oct 23, 2009

1. The problem statement, all variables and given/known data

A bicycle with a speed 12 km/h is driving along a leveled wet road. How much ahead the front axle (see picture) does the wheel jet the water that it picks up from the floor?The radius of the wheel is r = 35 cm. Let’s suppose that the drops of water that are separating from the highest point of the wheel are flying the farthest; and we suppose that the drops are not separating from the lower part of the wheel because of the mudguard of the wheel is preventing them. What is the solution for the bicycle without the mudguard under the same condition?

2. Relevant equations

∆y= y- y_0= v_0t- ½ gt²
∆x= x- x_0= v_0t

3. The attempt at a solution

First I calculated time:
∆y= y- y_0= v_0y*t- ½ gt²
y_0= 0
v_0y= 0
and I set for y= (-0.7m), because the drop is falling to the ground

y= -½ gt²
t= 0.38 s

Now I calculated the distance:
∆x= x- x_0= v_0x*t
x_0= 0
v_0x= 12 m/s
t= 0.38 s

x= v_0x*t
x= 4.53 m

Last edited: Oct 23, 2009
2. Oct 23, 2009

### willem2

It's 12 km/h, not 12 m/s. You didn't get the part without the mudguard. I think the furthest drops will escape before the highest point.

3. Oct 23, 2009

Yes, I made a typo, it's 12 km/h= 3.33 m/s!

And x= 1.27 m

Thank you very much!

4. Oct 23, 2009

Yeah, I have no idea how to approach this part! Can you give me a hint?

Thanks!

5. Oct 23, 2009

### willem2

If the water separates at an angle $\phi$ before the highest point, it will be at an altitude of $2R - R cos(\phi)$, it will have a speed of ........ (split in x and y components) and start out at a distance ............ behind the front axle.

Once you know that, it's just a 2d projectile problem: find the time of flight, and from that find the distance. The answer will depend on $\phi$ of course, and you need to find the maximum by differentiaton.