Solving Friction Problems: Homework Statement & Equations

[LoveandHate]

Homework Statement

A 2.5 kg cat is fired horizontally out of a cannon across a frozen lake. It is wearing steel tap shoes. The kinetic coefficient of friction is 0.010. If the cat's initial speed was 200 km/h, then:
a) does the cat make it all the way across the 1.0 km wide lake?
b) if so, what is its final speed on the far side of the lake?
c) if the coefficient of kinetic friction between the steel and ground on the far side of the lake is 0.50000, how far does the cat slide?

Homework Equations

F_g=ma
F_k=\mu_kF_N
F_NET=ma
v₂²=v_1²+2a\Deltad

The Attempt at a Solution

a) I figured out F_N by using F_g=ma and got 24.5 N [up]. I then used this to find F_k, which would equal F_NET. For this value, I got 0.245 N [W]. Then I found acceleration using F_NET=ma and got -0.098 m/s². I subbed all of these numbers into the the last formula and got about 15749.56 m. I think I may have used the last formula wrong because I assumed what v₂ is, but I needed to because I don't know what \Deltat is.

b) I assume that I will sub all of my calculations (the appropriate ones, of course) into the last formula and solve for v₂?

c) I have no idea how to start this one.

 

[Thaakisfox]

Your notation is a bit messy... So with the normal force and gravitational force you have a different acceleration. One is due to the friction "a" and the other is due to gravity "g". So you should write Fg=my instead... No what did you assume for v2? Think about the work-energy theorem ;)

 

[LoveandHate]

Your notation is a bit messy... So with the normal force and gravitational force you have a different acceleration. One is due to the friction "a" and the other is due to gravity "g". So you should write Fg=my instead... No what did you assume for v2? Think about the work-energy theorem ;)

we haven't learned that yet! and I'm confused by what you said.