Question

Two groups of canoeists meet in the middle of a lake. After a brief visit, a person in canoe 1 pushes on canoe 2 with a force of 46 N to separate the canoes. If the mass of canoe 1 and its occupants is 130 kg, and the mass of canoe 2 and its occupants is 250 kg, find the momentum of each canoe after 1.20 s of pushing.

Answer 1

Answer:

Momentum of canoe 1 is 55.12 kgm/s

Momentum of canoe 2 is 55.12 kgm/s

Explanation:

From Newton's Third law the force acting on both canoe's is 46 N

F = 46 N

F = ma

$\\\Rightarrow a=\frac{F}{m}\\\Rightarrow a=\frac{46}{130}\\\Rightarrow a=0.354\ m/s^2$

The acceleration of canoe 1 is 0.354 m/s²

t = Time taken

u = Initial velocity = 0

v = Final velocity

a = Acceleration

$a=\frac{F}{m}\\\Rightarrow a=\frac{46}{250}\\\Rightarrow a=0.184\ m/s^2$

The acceleration of canoe 2 is 0.184 m/s²

$v=u+at\\\Rightarrow v=0+0.354\times 1.2\\\Rightarrow v=0.424\ m/s$

The velocity of canoe 1 is 0.424 m/s

$v=u+at\\\Rightarrow v=0+0.184\times 1.2\\\Rightarrow v=0.2208\ m/s$

The velocity of canoe 2 is 0.2208 m/s

Momentum

p = mv

$p=130\times 0.424\\\Rightarrow p=55.12\ kgm/s$

Momentum of canoe 1 is 55.12 kgm/s

$p=250\times 0.2208\\\Rightarrow p=55.12\ kgm/s$

Momentum of canoe 2 is 55.12 kgm/s