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blsea [12.9K]
3 years ago
10

BIO EST The archerfish (genus Toxotes) preys on land-based insects inhabiting tree limbs above the water. It has the ability to

shoot a jet of water droplets from its specialized mouth, which can knock an insect down and onto the water surface. The archerfish typically shoots the water jet at an angle of 70‚àò above the horizontal. These droplets can reach a height of 10 m! Taking the angle to be 70‚àò and the maximum height to be 10 m, estimate the initial speed of the water droplets.
Physics
1 answer:
monitta3 years ago
3 0

Answer:

The initial speed of the water droplets is approximately 14.904 meters per second.

Explanation:

We can describe the water jet from archerfish as part of parabolic motion, which consists of the superposition of two different motions. First, an horizontal motion at constant velocity and, second, a free fall motion. The maximum height is reached when vertical component of speed is zero. The equation of motion is described below:

v^{2} = v_{o}^{2}\cdot \sin^{2} \theta + 2\cdot g \cdot (y-y_{o})

Where:

v_{o} - Initial speed of the water jet, measured in meters per second.

v - Current speed of the water jet, measured in meters per second.

g - Gravitational acceleration, measured in meters per square second.

y_{o} - Initial height, measured in meters.

y - Current height, measured in meters.

Now we clear the initial speed within equation:

v_{o}^{2} =\frac{v^{2}-2\cdot g\cdot (y-y_{o})}{\sin^{2}\theta}

v_{o} = \sqrt{\frac{v^{2}-2\cdot g\cdot (y-y_{o})}{\sin^{2}\theta} }

If we know that v = 0\,\frac{m}{s}, g = -9.807\,\frac{m}{s^{2}}, y = 10\,m, y=0\,m and \theta = 70^{\circ}, the initial speed of the water droplets is:

v_{o} = \sqrt{\frac{\left(0\,\frac{m}{s} \right)^{2}-2\cdot \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (10\,m-0\,m)}{\sin^{2}70^{\circ}} }

v_{o} \approx 14.904\,\frac{m}{s}

The initial speed of the water droplets is approximately 14.904 meters per second.

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LOTS OF POINTSA rocket of mass 40 000 kg takes off and flies to a height of 2.5 km as its engines produce 500 000 N of thrust.
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Explanation:

This is a problem that encompasses the work and principle of energy conservation.

In this way, we establish the equation for the principle of conservation and energy.

i)

E_{k1}+W_{1-2}=E_{k2}\\where:\\E_{k1}= kinetic energy at moment 1\\W_{1-2}= work between moments 1 and 2.\\E_{k2}= kinetic energy at moment 2.

W_{1-2}= (F*d) - (m*g*h)\\W_{1-2}=(500000*2.5*10^3)-(40000*9.81*2.5*10^3)\\W_{1-2}= 269*10^6[J] or 269 [MJ]

At that point the speed 1 is equal to zero, since the maximum height achieved was 2.5 [km]. So this calculated work corresponds to the energy of the rocket.

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8 0
3 years ago
A certain spring has a spring constant k1 = 660 N/m as the spring is stretched from x = 0 to x1 = 35 cm. The spring constant the
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(a) The equation for the work done in stretching the spring from x1 to x2 is ¹/₂K₂Δx².

(b) The work done, in stretching the spring from x1 to x2 is 11.25 J.

(c) The work, necessary to stretch the spring from x = 0 to x3 is 64.28 J.

<h3>Work done in the spring</h3>

The work done in stretching the spring is calculated as follows;

W = ¹/₂kx²

W(1 to 2) = ¹/₂K₂Δx²

W(1 to 2)  =  ¹/₂(250)(0.65 - 0.35)²

W(1 to 2)  = 11.25 J

W(0  to 3) = ¹/₂k₁x₁² + ¹/₂k₂x₂² + ¹/₂F₃x₃

W(0  to 3) = ¹/₂(660)(0.35)² + ¹/₂(250)(0.65 - 0.35)² + ¹/₂(105)(0.89 - 0.65)

W(0  to 3) = 64.28 J

Learn more about work done here: brainly.com/question/25573309

#SPJ1

6 0
2 years ago
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