Answer:
Da=(1/4)Db
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s²
When s = Da, t = t

When s = Db, t = 2t

Dividing the two equations

Hence, Da=(1/4)Db
Answer:
see below
Explanation:
You will need t find the volume of the sphere
4/3 pi r^3 divide into the mass
1431 / (4/3 pi (5.8)^3) = 14 gm /cm^3
The amount of work done in emptying the tank by pumping the water over the top edge is 163.01* 10³ ft-lbs.
Given that, the tank is 8 feet across the top and 6 feet high
By the property of similar triangles, 4/6 = r/y
6r = 4y
r = 4/6*y = 2/3*y
Each disc is a circle with area, A = π(2/3*y)² = 4π/9*y²
The weight of each disc is m = ρw* A
m = 62.4* 4π/9*y² = 87.08*y²
The distance pumped is 6-y.
The work done in pumping the tank by pumping the water over the top edge is
W = 87.08 ∫(6-y)y² dy
W = 87.08 ∫(6y³ - y²) dy
W = 87.08 [6y⁴/4 - y³/3]
W = 87.08 [3y⁴/2- y³/3]
The limits are from 0 to 6.
W = 87.08 [3*6⁴/2 - 6³/3] = 87.08* [9*6³ - 2*36] = 87.08(1872) = 163013.76 ft-lbs
The amount of work done in emptying the tank by pumping the water over the top edge is 163013.76 ft-lbs.
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Answer:
2917.4 m/s
Explanation:
From the question given above, the following data were:
Gravitational acceleration of the Moon (g) = 0.25 times the gravitational acceleration of the earth
Radius (r) of the Moon = 1737 Km
Escape velocity (v) =?
Next, we shall determine the gravitational acceleration of the Moon. This can be obtained as follow:
Gravitational acceleration of the earth = 9.8 m/s²
Gravitational acceleration of the Moon (g) = 0.25 times the gravitational acceleration of the earth
= 0.25 × 9.8 = 2.45 m/s²
Next, we shall convert 1737 Km to metres (m). This can be obtained as follow:
1 Km = 1000 m
Therefore,
1737 Km = 1737 Km × 1000 m / 1 Km
1737 Km = 1737000 m
Thus, 1737 Km is equivalent to 1737000 m
Finally, we shall determine the escape velocity of the rocket as shown below:
Gravitational acceleration of the Moon (g) = 2.45 m/s²
Radius (r) of the moon = 1737000 m
Escape velocity (v) =?
v = √2gr
v = √(2 × 2.45 × 1737000)
v = √8511300
v = 2917.4 m/s
Thus, the escape velocity is 2917.4 m/s