A 3.0-kg ball moving eastward at 4.0 m/s suddenly collides with and sticks to a 5.0-kg ball moving northward at 3.0 m/s. what is
1 answer:
Magnitude of the momentum of this system just after the collision = 19.2Kgm/s
<h3>What is law of conservation of momentum?</h3>Law of conservation of momentum states that the total momentum after the collision must be equal to the total momentum before the collision.
The momentum of each ball is given by:
p = mv
where m is the mass of the ball and v its velocity.
The momentum of ball 1 is:
p = mv
= (3.0 kg)(4.0 m/s)
= 12.0 kg m/s in the eastward direction
The momentum of ball 2 is:
p = mv
= (5.0 kg)(3.0 m/s)
= 15.0 kg m/s in the northward direction
The two momenta are in perpendicular directions, so the magnitude of the total momentum can be found as:
and due to the law of conservation of the momentum, this is also equal to the total momentum after the collision.
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Answer:
Step-by-step explanation:
We want to find the equation of a circle with a center at (7, 2) and a point on the circle at (2, 5).
First, recall that the equation of a circle is given by:
Where (<em>h, k</em>) is the center and <em>r</em> is the radius.
Since our center is at (7, 2), <em>h</em> = 7 and <em>k</em> = 2. Substitute:
Next, the since a point on the circle is (2, 5), <em>y</em> = 5 when <em>x</em> = 2. Substitute:
Solve for <em>r: </em>
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Simplify. Thus:
Finally, add:
We don't need to take the square root of both sides, as we will have the square it again anyways.
Therefore, our equation is:
For this case we have the following quadratic functions:
Revenue:
Cost:
Then, we observe that the profit is given by the following mathematical relationship:
Substituting values we have:
Making the corresponding calculations we have:
Answer:
An expression that represents the profit is: