Question:
A small rocket is launched vertically upward from the edge of a cliff 80 ft off the ground at a speed of 69 ft/s. Its height (in feet) above the ground is given by [tex]h(t) = - 25t^2 + 200t + 400[/tex] where t represents time measured in seconds.
Assuming the rocket is launched at t=0, what is an appropriate domain for h?
Answer:
[tex]0 \le t \le 9.66[/tex]
Explanation:
Given
[tex]h(t) = - 25t^2 + 200t + 400[/tex]
Required
Determine the domain of h
The initial value of t is 0.
i.e.
[tex]t = 0[/tex] --- This is given in the question
To determine the final value, we simply solve for t in [tex]h(t) = - 25t^2 + 200t + 400[/tex]
Rewrite the expression:
[tex]- 25t^2 + 200t + 400=0[/tex]
Divide through by -25
[tex]\frac{-25t^2}{-25} + \frac{200t}{-25} + \frac{400}{25}=\frac{0}{-25}[/tex]
[tex]t^2 - 8t - 16 = 0[/tex]
Using quadratic formula:
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a= 1[/tex] [tex]b = -8[/tex] and [tex]c = -16[/tex]
The expression becomes:
[tex]t = \frac{-(-8)\±\sqrt{(-8)^2 - 4*1*(-16)}}{2*1}[/tex]
[tex]t = \frac{8\±\sqrt{64+ 64}}{2}[/tex]
[tex]t = \frac{8\±\sqrt{128}}{2}[/tex]
[tex]\sqrt{128} = 11.31[/tex]
So, we have:
[tex]t = \frac{8\±11.31}{2}[/tex]
Split
[tex]t = \frac{8+11.31}{2}\ or\ t = \frac{8-11.31}{2}[/tex]
[tex]t = \frac{19.31}{2}\ or\ t = \frac{-3.31}{2}[/tex]
[tex]t = 9.66\ or\ t = -1.66[/tex]
But time can't be negative.
So:
[tex]t = 9.66[/tex]
Hence, the domain is:
[tex]0 \le t \le 9.66[/tex]
Bonus: A runner has a speed of 25 m/s. They see the finish line and speed up to 30 m/s. This happens in 5
seconds. If the runner has a mass of 75 kg, with what force did the runner cross the finish line?
Describe mechanical energy in your own words
Answer:
motion......
movement.....
Answer:
the energy possessed by a body due to its motion or position is called mechanical engergy
1.
What is force & how is it measured?
Answer:
Force is measured using either the English System of Measurements or the International System of Units A force can cause an object with mass to change its velocity It is measured in the SI unit of newtons and represented by the symbol F.
Explanation:
What three forces are always in effect?
Answer:The gravitational force is defined in Uniform Circular Motion and Gravitation, electric force in Electric Charge and Electric Field, magnetic force in Magnetism, and nuclear forces in Radioactivity and Nuclear Physics. On a macroscopic scale, electromagnetism and gravity are the basis for all forces.
Explanation:
Answer:
The gravitational force is defined in Uniform Circular Motion and Gravitation, electric force in Electric Charge and Electric Field, magnetic force in Magnetism, and nuclear forces in Radioactivity and Nuclear Physics. On a macroscopic scale, electromagnetism and gravity are the basis for all forces.
An object travels at 3.06 m distance with uniform acceleration in this interval it's velocity increases by 0.18 and it's average velocity over the interval was 0.34 m/s what is the acceleration?
Given that,
Distance travelled, d = 3.06 m
Final velocity, v = 0.18 m/s
Average velocity of the object, V = 0.34 m/s
To find,
The acceleration of the object.
Solution,
Let t is the time in which it covers distance d. Average velocity is given by distance covered divided by time.
[tex]V=\dfrac{d}{t}\\\\t=\dfrac{d}{V}\\\\t=\dfrac{3.06}{0.34}\\\\t=9\ s[/tex]
Let a is the acceleration of the object. Using equation of motion to find it :
[tex]a=\dfrac{v-u}{t}\\\\a=\dfrac{0.18-0}{9}\\\\a=0.02\ m/s^2[/tex]
So, the acceleration of the object is 0.02 m/s².
Find the value of x help asap
Answer:
46 degrees
Explanation:
90+44+x=180
44+x=90
x=46
Answer:well isn't it 90 like it said on the image?
Explanation?????
The graph represents velocity over time.
A graph with horizontal axis time (seconds) and vertical axis velocity (meters per second). A line runs from 0 seconds 2 meters to 100 seconds 22 meters.
What is the acceleration?
–0.2 m/s2 I did it on edge 2020
Answer:
the answer is C
Explanation:
i got it wrong the first time because the answer above says -0.2 but its actually 0.2
i hope this helps
Two plates are 2cm apart, a potential difference of 10 V is applied
between them, find the electric field between the plates.
Answer:
The electric field betwee the plates is 500 V/m
Explanation:
Voltage
The electrical potential difference V between the two plates is expressed as
V=Ed
Where:
E = Electric field strength
d = Distance between the plates
It's expressed in Joules/coulomb, Volts/m or equivalent units.
The plates are separated d=2 cm and a potential difference V=10 V is applied. The electric field strength between the plates can be calculated by solving the formula for E:
[tex]\displaystyle E=\frac{V}{d}[/tex]
Converting cm to m: d=2 / 100 = 0.02 m
[tex]\displaystyle E=\frac{10\ V}{0.02\ m}[/tex]
Dividing:
E = 500 V/m
The electric field betwee the plates is 500 V/m
Should genetic genealogy be used to solve crimes ? Yes or no and why?
Answer:
yes
Explanation:
because it will help find who did the crime and it can also open jobs and opportunities for the people who likes sicnenae
A 5 kilogram block is dropped from a height of 3 meters and falls straight to the ground. What is the work done by the force of gravity?
Answer:
Workdone = 147Nm
Explanation:
Given the following data;
Mass = 5kg
Height = 3m
We know that acceleration due to gravity is 9.8m/s²
First of all, we would find the force applied;
[tex] Force = mass * acceleration [/tex]
Force = 5*9.8
Force = 49N
Now, to find the workdone;
[tex] Workdone = force * distance [/tex]
Substituting into the equation, we have;
Workdone = 49 * 3
Workdone = 147Nm
A car possesses 20 000 units of momentum. What would be the car's new momentum if its mass was doubled
I'm
Answer:
40 000 units of momentum
Explanation:
Assuming that the mass is doubled and the velocity stays constant the new momentum will be doubled the original momentum.
The amount of _______ that occurs when a sound wave encounters a barrier depends on the wave's length.
What are some human causes for global warming?
Answer: At present, humans are putting an estimated 9.5 billion metric tons of carbon into the atmosphere each year by burning fossil fuels, and another 1.5 billion through deforestation and other land cover changes
Explanation: