Does baby oil have a high or low velocity?

Sand is pouring out of a pipe and is forming a conical pile on the ground. The radius of the pile is increasing at a rate of 2 f

Anton [14]

Answer:

$a)\ V=3053.628059 \ ft^3$

$b)\ V'=1017.876\ ft^3/day$

Explanation:

<u>Rate of Change</u>

The volume of a cone of radius r and height h is given by

$\displaystyle V=\frac{\pi r^2h}{3}$

The height is said to be 1/2 of the radius, thus

$\displaystyle V=\frac{\pi r^2\cdot r}{2\cdot 3}$

$\displaystyle V=\frac{\pi r^3}{6}$

a) Knowing r=18 feet, the volume is

$\displaystyle V=\frac{\pi 18^3}{6}$

$V=3053.628059 \ ft^3$

b) The rate of change of the volume is computed by taking the derivative of both sides respect to the time

$\displaystyle V'=3\frac{\pi r^2}{6}r'$

$\displaystyle V'=\frac{\pi r^2}{2}r'$

Where r' is the given rate of change of the radius: 2 feet/day.

Now we compute

$\displaystyle V'=\frac{\pi 18^2}{2}\cdot 2=1017.876$

$\boxed{V'=1017.876\ ft^3/day}$

6 0

3 years ago

A 15.0 kg fish swimming at 1.10 m/s suddenly gobbles up a 4.50 kg fish that is initially stationary. Ignore any drag effects of

Nana76 [90]

Answer

given.

Mass of big fish = 15 Kg

speed of big fish = 1.10 m/s

mass of the small fish = 4.50 Kg

speed of the fish after eating small fish =?

a) using conservation of momentum

m₁v₁ + m₂v₂ = (m₁+m₂) V

15 x 1.10 + 4.50 x 0 = (15 + 4.5)V

16.5 = 19.5 V

V = 0.846 m/s

b) Kinetic energy before collision

$KE_1 = \dfrac{1}{2}m_1v_1^2 + \dfrac{1}{2}m_2v_2^2$

$KE_1 = \dfrac{1}{2}\times 15 \times 1.1^2 + \dfrac{1}{2}m_2\times 0^2$

KE₁ = 9.075 J

Kinetic energy after collision

$KE_2= \dfrac{1}{2}(15+4.5)\times 0.846^2$

KE₂ = 6.98 J

Change in KE = 6.98 - 9.075 = -2.096 J

hence,

mechanical energy was dissipated during this meal = -2.096 J

5 0

3 years ago

Which describes the relationship between potential and kinetic energy of a ball thrown up in the air as it falls back to the gro

Gekata [30.6K]

The answer is c, because ball is falling so its gravitationl potential energy decreases, but it kinetic energy increases. Energy is always conserved.

7 0

3 years ago

You are throwing a stone straight-up in the absence of air friction. The stone is caught at the same height from which it was th

balu736 [363]

Answer:

A. True

Explanation:

When a stone is thrown straight-up, it has an initial velocity which decreases gradually as the stone move to maximum height due to constant acceleration due to gravity acting downward on the stone, at the maximum height the final velocity of the stone is zero. As the stone descends the velocity starts to increase and becomes maximum before it hits the ground.

Height of the motion is given by;

$H = \frac{u^2}{2g}$

g is acceleration due to gravity which is constant

H is height traveled

u is the speed of throw, which determines the value of height traveled.

Therefore, when the stone is caught at the same height from which it was thrown in the absence of air resistance, the speed of the stone when thrown will be equal to the speed when caught.

7 0

3 years ago

2. In the pendulum lab, the period (swing time) was O a. the independent variable O b.graphed on the vertical-axis O c.graphed o

Nadya [2.5K]

B is appropriate answer

7 0

3 years ago