Answer:
765 J
Step-by-step explanation:
We are given;
Mass of bucket = 30 kg
Mass of rope = 0.3 kg/m
height of building= 30 meter
Now,
work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand
Or W = W1 + W2
Work done in lifting the rope is given as,
W1 = Force x displacement
W1 = (30,0)∫(0.2x .dx)
Integrating, we have;
W1 = [0.2x²/2] at boundary of 30 and 0
W1 = 0.1(30²)
W1 = 90 J
work done in lifting the sand is given as;
W2 = (30,0)∫(F .dx)
F = mx + c
Where, c = 30 - 15 = 15
m = (30 - 15)/(30 - 0)
m = 15/30 = 0.5
So,
F = 0.5x + 15
Thus,
W2 = (30,0)∫(0.5x + 15 .dx)
Integrating, we have;
W2 = (0.5x²/2) + 15x at boundary of 30 and 0
So,
W2 = (0.5 × 30²)/2) + 15(30)
W2 = 225 + 450
W2 = 675 J
Therefore,
work done lifting the bucket (sand and rope) to the top of the building,
W = 90 + 675
W = 765 J
Answer:
Penguins can swim at a speed of 19.77 miles per hour.
Step-by-step explanation:
Since penguins can swim at speeds of up to 29 feet per second, to convert this speed to miles per hour, knowing that 1 mile is equal to 5280 feet, the following calculation must be performed:
1 hour = 60 minutes
1 minute = 60 seconds
1 hour = 60x60 seconds = 3,600 seconds
29 x 3,600 = feet per hour = 104,400
104,400 / 5,280 = miles per hour = 19.77
Thus, penguins can swim at a speed of 19.77 miles per hour.
108÷9•(-12)÷6-(100÷5) the answer is -44
7/8 gallon of water/ (1/2 hr)= 1.75 gallons of water/ hr.
The swimming pool is leaking 1.75 gallons of water/ hr.
Hope this helps~
