Answer:
V = 108 ft³
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Geometry</u>
Volume of a Rectangular Prism Formula: V = lwh
- <em>l</em> is length
- <em>w</em> is width
- <em>h</em> is height
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
<em>l</em> = 4 ft
<em>w</em> = 3 ft
<em>h</em> = 9 ft
<u>Step 2: Find Volume</u>
- Substitute in variables [Volume of a Rectangular Prism Formula]: V = (4 ft)(3 ft)(9 ft)
- Evaluate [Order of Operations]: V = 108 ft³
Simply divide 15.7 by 6.28 to get 2.5 :) easy peasy pumpkin pie
Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
Answer:
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Step-by-step explanation:
