1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
STatiana [176]
3 years ago
13

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 30 ft/s. Its height

in feet after t seconds is given by y=30t-10t^2. a) Find the average velocity over the time interval [2,2+ h] where h is given as follows: h= 0.1 ______ ft/s h= 0.01 _____ ft/s h= 0.001 _____ ft/s Estimate the instantaneous velocity when t= 2 _____ ft/s
Mathematics
1 answer:
Crank3 years ago
8 0

Answer:

a) h = 0.1: \bar v = -11\,\frac{ft}{s}, h = 0.01: \bar v = -10.1\,\frac{ft}{s}, h = 0.001: \bar v = -10\,\frac{ft}{s}, b) The instantaneous velocity of the ball when t = 2\,s is -10 feet per second.

Step-by-step explanation:

a) We know that y = 30\cdot t -10\cdot t^{2} describes the position of the ball, measured in feet, in time, measured in seconds, and the average velocity (\bar v), measured in feet per second, can be done by means of the following definition:

\bar v = \frac{y(2+h)-y(2)}{h}

Where:

y(2) - Position of the ball evaluated at t = 2\,s, measured in feet.

y(2+h) - Position of the ball evaluated at t =(2+h)\,s, measured in feet.

h - Change interval, measured in seconds.

Now, we obtained different average velocities by means of different change intervals:

h = 0.1\,s

y(2) = 30\cdot (2) - 10\cdot (2)^{2}

y (2) = 20\,ft

y(2.1) = 30\cdot (2.1)-10\cdot (2.1)^{2}

y(2.1) = 18.9\,ft

\bar v = \frac{18.9\,ft-20\,ft}{0.1\,s}

\bar v = -11\,\frac{ft}{s}

h = 0.01\,s

y(2) = 30\cdot (2) - 10\cdot (2)^{2}

y (2) = 20\,ft

y(2.01) = 30\cdot (2.01)-10\cdot (2.01)^{2}

y(2.01) = 19.899\,ft

\bar v = \frac{19.899\,ft-20\,ft}{0.01\,s}

\bar v = -10.1\,\frac{ft}{s}

h = 0.001\,s

y(2) = 30\cdot (2) - 10\cdot (2)^{2}

y (2) = 20\,ft

y(2.001) = 30\cdot (2.001)-10\cdot (2.001)^{2}

y(2.001) = 19.99\,ft

\bar v = \frac{19.99\,ft-20\,ft}{0.001\,s}

\bar v = -10\,\frac{ft}{s}

b) The instantaneous velocity when t = 2\,s can be obtained by using the following limit:

v(t) = \lim_{h \to 0} \frac{x(t+h)-x(t)}{h}

v(t) =  \lim_{h \to 0} \frac{30\cdot (t+h)-10\cdot (t+h)^{2}-30\cdot t +10\cdot t^{2}}{h}

v(t) =  \lim_{h \to 0} \frac{30\cdot t +30\cdot h -10\cdot (t^{2}+2\cdot t\cdot h +h^{2})-30\cdot t +10\cdot t^{2}}{h}

v(t) =  \lim_{h \to 0} \frac{30\cdot t +30\cdot h-10\cdot t^{2}-20\cdot t \cdot h-10\cdot h^{2}-30\cdot t +10\cdot t^{2}}{h}

v(t) =  \lim_{h \to 0} \frac{30\cdot h-20\cdot t\cdot h-10\cdot h^{2}}{h}

v(t) =  \lim_{h \to 0} 30-20\cdot t-10\cdot h

v(t) = 30\cdot  \lim_{h \to 0} 1 - 20\cdot t \cdot  \lim_{h \to 0} 1 - 10\cdot  \lim_{h \to 0} h

v(t) = 30-20\cdot t

And we finally evaluate the instantaneous velocity at t = 2\,s:

v(2) = 30-20\cdot (2)

v(2) = -10\,\frac{ft}{s}

The instantaneous velocity of the ball when t = 2\,s is -10 feet per second.

You might be interested in
What is the rule for the reflection?
mote1985 [20]

Answer:

Step-by-step explanation:

it’s the last one

6 0
3 years ago
18 is 60% of what number
LuckyWell [14K]
Let n be the number 18=60% of n
18=0.6n
18/0.6=n
30=n
3 0
3 years ago
Read 2 more answers
A polyhedron with two parallel congruent faces called bases connected by parallelogram faces is called a...
lisov135 [29]

Answer:

right prism

Step-by-step explanation:

If the faces are rectangles, then this prism is called a "right prism"

4 0
3 years ago
3. Which number is closest to zero on<br> the number line?<br> A -3/8<br> B 3/4<br> C 0.3<br> D 0.50
insens350 [35]

Answer:

0.3

Step-by-step explanation:

A. .375

B. .75

C. .3

D. .5

6 0
3 years ago
Read 2 more answers
Pregunta 4 (1 punto)
Yuliya22 [10]

Answer:

7....................

3 0
3 years ago
Read 2 more answers
Other questions:
  • Neela’s clock is broken. The minute hand rotates around the clock correctly, but the hour hand is stuck in the three o’clock pos
    12·1 answer
  • FIRST TO ANSWER GETS BRAINLIEST
    7·2 answers
  • If there are 10 people in a race how many ways can 1st 2nd 3rd places be awarded
    10·1 answer
  • A deli sells 44 cups of soup for every 60 sandwiches. At this rate,how many cups of soup will be sold for every 15 sandwiches
    5·2 answers
  • Someone pls help me with this question
    14·2 answers
  • if u take my points i will hack you but PLZ i need help I'm taking a math test and frgt to study if I get all four correct I wil
    8·1 answer
  • Find the equation of the straight line passing through P(-2,1) and parallel to the line with equation 2x-3y=1
    10·1 answer
  • Say you are considering two loans. Loan F has a nominal interest rate of 5. 66%, compounded monthly. Loan G has a rate of 6. 02%
    7·1 answer
  • What is 12 to the exponent 263845
    6·2 answers
  • What is the value of x<br><br>find the value of f​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!