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
12345 [234]
3 years ago
10

A bucket that weighs 6 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket is f

illed with 36 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done W in pulling the bucket to the top of the well.
Mathematics
1 answer:
zaharov [31]3 years ago
4 0

Answer:

3200 ft-lb

Step-by-step explanation:

To answer this question, we need to find the force applied by the rope on the bucket at time t

At t=0, the weight of the bucket is 6+36=42 \mathrm{lb}

After t seconds, the weight of the bucket is 42-0.15 t \mathrm{lb}

Since the acceleration of the bucket is the force on the bucket by the rope is equal to the weight of the bucket.

If the upward direction is positive, the displacement after t seconds is x=1.5 t

Since the well is 80 ft deep, the time to pull out the bucket is \frac{80}{2}=40 \mathrm{~s}

We are now ready to calculate the work done by the rope on the bucket.

Since the displacement and the force are in the same direction, we can write

W=\int_{t=0}^{t=36} F d x

Use x=1.5 t and F=42-0.15 t

W=\int_{0}^{36}(42-0.15 t)(1.5 d t)

=\int_{0}^{36} 63-0.225 t d t

=63 \cdot 36-0.2 \cdot 36^{2}-0=3200 \mathrm{ft} \cdot \mathrm{lb}

=\left[63 t-0.2 t^{2}\right]_{0}^{36}

W=3200 \mathrm{ft} \cdot \mathrm{lb}

You might be interested in
Which point represents the unit rate?
uysha [10]
C <span>represents the unit rate

hope that helps</span>
6 0
3 years ago
Read 2 more answers
How do you answer this question:
Maurinko [17]
66527273848 A. Aaaaaaaaaaaaaaaaa
5 0
2 years ago
Find the slope and y-intercept of each equation<br><br>y = x - 3<br>m = ?<br>b = ?​
barxatty [35]

Answer:

m = 1

b= -3

Step-by-step explanation:

4 0
2 years ago
Negative 20 minus Positive 17
nikitadnepr [17]

Answer:

-3

Step-by-step explanation:

-20+17=-3

no hate but that’s simple math why does it say you’re in high school lol

6 0
2 years ago
Read 2 more answers
A square has a side lengths of 9, use the pythagorean theorem to find the length of the diagonal
Semmy [17]

diagonal = 9√2 ≈ 12.73

the diagonal splits the square into 2 right triangles with the hypotenuse being the diagonal of the square

using Pythagoras' identity

d = √(9² + 9²) = √162 = 9√2 ≈ 12.73 ( to 2 dec. places )


5 0
3 years ago
Other questions:
  • What is the 4th term in the sequence? <br><br> C(1)=56<br> C(n)= c(n-1)•1/2
    13·1 answer
  • (The equation of line L is Y=3X+2) Write the slope intercept form of the equation of the line passing through (3,2) and parallel
    15·1 answer
  • after Megan walked 5 miles high activity tracker had taunted 9780 stats activity tracker had counted 11928 steps after he walk 6
    11·1 answer
  • Aisha can use the expression 120 divided by 10 to determine the solution to which problem?
    7·2 answers
  • you plan to open a lemonade stand near where you live. The cost to buy the wood is $60 and the cost to make the lemonade is $3 p
    14·1 answer
  • Cuánto es mínimo común múltiplo de 87 y 69​
    12·1 answer
  • Find the missing value of this triangle
    13·2 answers
  • 4x/3=8 what is x? PLEASE HURRY DUE TOMORROW!!!!!!
    6·1 answer
  • Write an equation for the line that has a slope of -4 and passes through the point (2,-3)
    8·1 answer
  • A six-sided number cube is rolled 300 times. The results are 120 even numbers and 180 odd numbers.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!