# Two groups of canoeists meet in the middle of a lake. 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, after 1.20s?

Canoe 1 :

Canoe 2 :

The key to answering this question is comprehending Newton's Third Law:

"Every action will have and equal and opposite reaction"

This implies that the canoeist is pushing the other canoe at 46N as well as himself when pushing with 46N.

Newton's Second Law and the momentum formula must be used to determine the final velocity and momentum on Canoe 1 (after 1.20 seconds).

This is your final velocity. Next, multiply this acceleration by the given time duration to find velocity (one of the acceleration unit's seconds will be canceled, leaving you with m/s).

The procedure is the same for determining the second canoe's velocity and momentum, but you need to make sure that you include its mass in your calculations.

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To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. We'll use this law to find the acceleration of the canoes after the push, and then use kinematic equations to determine their final velocity.

First, let's find the acceleration:

[ F = ma ] [ 46 , \text{N} = (m_1 + m_2) \times a ] [ a = \frac{46 , \text{N}}{130 , \text{kg} + 250 , \text{kg}} ] [ a ≈ 0.117 , \text{m/s}^2 ]

Now, let's use the kinematic equation to find the final velocity:

[ v = u + at ]

Where:

- ( v ) is the final velocity
- ( u ) is the initial velocity (which we assume to be zero)
- ( a ) is the acceleration
- ( t ) is the time

For both canoes, the final velocity will be the same, so we'll use the same equation for both.

[ v = 0 + (0.117 , \text{m/s}^2) \times 1.20 , \text{s} ] [ v ≈ 0.14 , \text{m/s} ]

Therefore, after 1.20 seconds, both canoes will have a final velocity of approximately 0.14 m/s.

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To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force exerted on canoe 2 will cause it to accelerate away from canoe 1.

First, we need to calculate the acceleration of canoe 2 using Newton's second law:

[ F = ma ]

Where:

- ( F ) is the force exerted on canoe 2 (46 N)
- ( m ) is the mass of canoe 2 and its occupants (250 kg)
- ( a ) is the acceleration of canoe 2

[ a = \frac{F}{m} = \frac{46, \text{N}}{250, \text{kg}} ] [ a = 0.184, \text{m/s}^2 ]

Now, since both canoes are involved in the interaction, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. So, while canoe 2 is accelerating away from canoe 1, canoe 1 will also experience an equal and opposite acceleration towards canoe 2.

To find the velocity of canoe 1 after 1.20 seconds, we use the formula:

[ v = u + at ]

Where:

- ( v ) is the final velocity of canoe 1
- ( u ) is the initial velocity of canoe 1 (which we assume to be 0 since it starts from rest)
- ( a ) is the acceleration of canoe 1 towards canoe 2
- ( t ) is the time (1.20 seconds)

[ v = 0 + (0.184, \text{m/s}^2)(1.20, \text{s}) ] [ v = 0.221, \text{m/s} ]

So, after 1.20 seconds, canoe 1 will have a velocity of 0.221 m/s towards canoe 2.

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