The momentum of an object is given by the product between its mass and its velocity:

where m is the mass and v the velocity.
For the object in our problem, m=10 kg and v=10 m/s, therefore its momentum is

So, the correct answer is B).
Answer: 459.14 N
Explanation:
from the question, we have
diameter = 10 m
radius (r) = 5 m
weight (Fw) = 670 N
time (t) = 8 seconds
Circular motion has centripetal force and acceleration pointing perpendicular and inwards of the path, therefore we apply the equation below
∑ F = F c = F w − Fn ..............equation 1
Fn = Fw − Fc = mg − (mv^2 / r) ...................equation 2
substituting the value of v as (2πr / T) we now have
Fn = mg − (m(2πr / T )^2) / r
Fn= mg − (4(π^2)mr / T^2) ..........equation 3
Fw (mass of the person) = mg
therefore m = Fw / g
m = 670 / 9.8 = 68.367 kg
now substituting our values into equation 3
Fn = 670 - ( (4 x (π^2) x 68.367 x 5 ) / 8^2)
Fn = 670 - 210.86
Fn = 459.14 N
Answer:
The maximum volume is 1417.87 
Explanation:
<u>Optimization Using Derivatives</u>
We have a 24x30 inch piece of metal and we need to make a rectangular box by cutting a square from each corner of the piece and bending up the sides. The width of the piece is 24 inches and its length is 30 inches
When we cut a square of each corner of side x, the base of the box (after bending up the sides) will be (24-2x) and (30-2x), width and length respectively. The volume of the box is

Operating

To find the maximum value of V, we compute the first derivative and equate it to zero

Simplifying by 12

Completing squares


We have two values for x


The first value is not feasible because it will produce a negative width (24-2(13.58))=-6.16
We'll keep only the solution

The width is

The length is

And the height

The maximum volume is

Mechanical and chemical. Mechanical breaks down food into smaller pieces. Chemical breaks it down into simpler nutrients that can then be used by cells. Hope this helps!
Answer:
(a) Potential energy of the child is converted into the kinetic energy at the bottom off the slide and a part of which is lost into friction generating heat between the contact surfaces.
(b) 
Explanation:
Given:
- mass of the child,

- height of the slide,

- initial velocity of the child at the slide,

- final velocity of the child at the bottom of slide,

(a)
∴The initial potential energy of the child is converted into the kinetic energy at the bottom off the slide and a part of which is lost into friction generating heat between the contact surfaces.
Initial potential energy:



Kinetic energy at the bottom of the slide:



(b)
Now, the difference in the potential and kinetic energy is the total change in the thermal energy of the slide and the seat of her pants.
This can be given as:


