The work required is Wa = 2954112 J
Given:
swimming pool diameter = 14 m
length of sides = 4 m
height of water = 3 m
To Find:
work required to pump water
Solution: The radius of the swimming pool is
r = 14/2 = 7 m
The work is mathematically given as
W = Force x distance
Now force is mathematically given as
F = density x area x height of pool = p*(πr²)dx
Now the work done to pump all of the water over the side
W = ∫p*(πr²)(H-x)dx = ∫1000*9.81*(π*7^2)(4-x)dx
W = 64000*9.8π∫(4-x) dx = 64000*9.8π{4(3) - 3/2}
W = 2954112 J
So, work required is Wa = 2954112 J
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Answer:
516526.863 m
Explanation:
From the question given above, the following data were obtained:
Acceleration due to gravity (g) = 2.24 m/s²
Mass (M) = 8.96×10²¹ Kg
Gravitational constant (G) = 6.67×10¯¹¹Nm²/Kg²
Radius (r) =?
The radius of the planet can be obtained as follow:
g = GM/r²
2.24 = 6.67×10¯¹¹ × 8.96×10²¹ / r²
2.24 = 5.97632×10¹¹ / r²
Cross multiply
2.24 × r² = 5.97632×10¹¹
Divide both side by 2.24
r² = 5.97632×10¹¹ / 2.24
r² = 2.668×10¹¹
Take the square root of both side
r = √2.668×10¹¹
r = 516526.863 m
Thus, the radius of the planet is 516526.863 m
Answer:
A ball is thrown at an initial height of 5 feet with an initial upward velocity at 29 ft/s. lets assume that balls height h (in feet) after t seconds is give by:
<u>h= 5 + 29t -16t^2</u>
Explanation:
h= 5 + 29t -16t^2
a time when the ball's height will be 17 ft
17 = 5 + 29t -16t2
0 = -17 + 5 + 29t -16t2
0 = -12 + 29t - 16t2
Using the quadratic equation:
t = (-29±√(292-(4*(-16)*(-12))))÷2(-16)
= (-29±√(841 - 768))÷(-32)
= (-29±√(73))÷(-32)
= (-29 + 8.544)÷(-32) or (-29 - 8.544)÷(-32)
= (-20.456)÷(-32) or -37.544÷(-32)
= 0.64 or 1.17
So, the ball is at a height of 17 ft twice: once on the way up after 0.64 seconds and once on the way back down after 1.17 seconds.
Answer:
a
b
c
Explanation:
From the question we are told that
The Young modulus is 
The length is 
The area is 
Generally the force acting on the tibia is mathematically represented as
derived from young modulus equation
Now this force can also be mathematically represented as
So
substituting values
Since the tibia support half the weight then the force experienced by the tibia is
From the above equation the extension (compression) is mathematically represented as
substituting values
From the above equation the maximum force is
Answer:
I believe it's 8.09 seconds, but I'm rusty on my physics.
Explanation:
The equation for solving the time it takes for an object to fall is 
So multiply the distance times 2, and you get 642 meters. Then you divide by gravities acceleration constant, 9.8, and you get 65.51. Finally, 
, and you get 8.09 seconds.
I pulled the equation off of wikipedia and I'm unsure if it's the correct one, so hopefully this is correct. :/
