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strangeeyes
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Homework Statement
A 63kg student stands on 34kg cart that is free to move in any direction. The cart and student are moving together with a velocity of 3.2 m/s [W]. The student then starts to walk so that her velocity is 1.8 m/s [25 degrees W of N] relative to the floor. Calculate the new velocity of the cart.
mass of student = mg = 63kg
mass of cart = mc = 34kg
velocity of system = vs = 3.2 m/s [W]
velocity of student = vg = 1.8 m/s [25 W of N]
velocity of cart = ?
Homework Equations
p=p'
The Attempt at a Solution
[PLAIN]http://img338.imageshack.us/img338/4709/momdia.jpg
let 's' represent the system
the final momentum of the system is equal to the vector addition of the student (g) and the cart (c)
ps'= pc' +pg'
rearrange to find pc':
pc'=ps'-pg'
ps=ps'
=(mg+mc)vs
=310.4 kg * m/s [W]
-pg'=63(1.8)
=113.4 kg * m/s [25 E of S]
now using components:
[PLAIN]http://img571.imageshack.us/img571/2365/diamom.jpg
-pgx'=63(1.8)sin25
=47.3249 kg * m/s [E]
-pgy'=63(1.8)cos25
=102.78 kg * m/s
using Pythagorus
pc'^2=pgy'^2 + [ps' + (-pgx)]^2
pc'=282.439 kg * m/s
to find direction of pc':
angle =tan-1(102.78 / 262.475)
= 21.38 degrees
therefor the new velocity of the cart is:
vc'=pc'/mc
= 8.31 m/s [21.4 S of E]
am i wrong? that answer seems unlikely...
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