# Maximum kinetic friction-combined with a projectile problem

1. Feb 21, 2015

### Poetria

1. The problem statement, all variables and given/known data
A cannon at ground level is shooting emergency packets to people stranded on the roof of a flooded building of height H=125 meters. The corner of the building is located a distance D=50 meters from the cannon. It is desired that the incoming packets are flying tangent to the roof as shown so that they land gently with as little impact as possible and slide along to a stop.

Find the initial speed v0 and at what angle θ (in degrees) the cannon should be aimed to achieve the above scenario
If the roof has length L=30 meters (not shown) what is the minimum coefficient of kinetic friction between the food packets and the roof such that the packets do not slide off the other side?

2. Relevant equations

v^2(x)=v^2_i,x+2a*x(x−xi)

3. The attempt at a solution

I only have a problem with the third part but I think I have found my mistake. I have confused horizontal velocity with vertical velocity. I got a very strange value for mu, much too high.

When packets land on a roof, there is no vertical velocity involved and I have already computed the value for the horizontal: v=9.9.

0=9.9^2-2*a*30
a=1.6335

m*a=mu*m*g
a=mu*g
mu=1.6335/9.8
mu=0.1666836734693877551020408163265306122448979591836734

2. Feb 21, 2015

### Staff: Mentor

Looks correct.
Are you sure it is not 0.1666836734693877551020408163265306122448979591836733? You should round final results to reasonable precision.

3. Feb 21, 2015

### Poetria

Right. Many thanks. :)
It is my friend, Wolfram Alpha.