A boat can travel in still water at 56 m/s. If the boats sails directly across a river that flows at 126 m/s. What is the boats speed relative to the ground

Answer:

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Explanation:

The torque applied will be the average of the 3 torque calculated.

Torque = 12.01 Nm

Torque of a couple is the product of a force and its perpendicular distance to the direction of the force. Torque is synonymous to moment.

From the question, the given radius is 0.53m. The perpendicular distance for each torque will be 2 x 0.53 = 1.06 m

We will calculate for each torque

T1 = F1d

T1 = 8 x 1.06 = 8.48 Nm

T2 = F2d

T2 = 15 x 1.06 = 15.9 Nm

T3 = F3d

T3 = 11 x 1.06 = 11.66 Nm

The torque applied will be the average of the 3 torque calculated. That is,

Torque = (8.48 + 15.9 + 11.66)/3

Torque = 36.04 /3

Torque = 12.01 Nm

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We are given:

extension of the spring (x) = 10 cm OR 0.1 m

Force applied to keep it in position (F) = 500 N

Solving for the spring constant:

We know that F = kx (when the spring is extended)

replacing the variables with the given values

500 = k * 0.1

k = 5000 N/m

This means that to extend the spring by 1 m, we have to apply a force of 5000 N

Answer:

Bernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquidor gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.

Three properties of an ideal fluid that obey Bernoulli’s principle are :

1) incompressible

2) subjected to conservative forces

3) non - viscous

Bernoulli's principle  states that as the speed of moving fluid increases , the pressure within fluid decreases or it states that   if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity.

As we know that Bernoulli's principle is only valid for ideal fluids which have following properties :

1) Should be incompressible

2) subjected to conservative forces

3) It should be non - viscous which means there is no internal friction in the flow .

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Answer:

C

Explanation:

The most commonly accepted theory of muscle growth states that microscopic tears within a muscle activate an inflammatory response process that causes dormant cells to build and regenerate muscle tissue; this is option c.

It has negative consequences on the muscle, and it is also known as "microtrauma," which occurs as a result of muscle contraction and is a normal part of the muscle repair and growth process. Here, the fibers in the muscle are damaged, and in response, the body initiates a repair process. This leads to muscle growth and increased strength and is helpful for muscle repair.

Hence, the most commonly accepted theory of muscle growth states that microscopic tears within a muscle activate an inflammatory response process that causes dormant cells to build and regenerate muscle tissue; this is option c.

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Answer:

(a) [tex]Probability = 0.7599[/tex]

(b) [tex]Probability = 0.2646[/tex]

Explanation:

Represent losing with L and winning with W.

So:

[tex]L = 0.7[/tex] --- Given

[tex]n = 4[/tex]

Probability of winning would be:

[tex]W = 1 - L[/tex]

[tex]W = 1 - 0.7[/tex]

[tex]W = 0.3[/tex]

The question illustrates binomial probability and will be solved using the following binomial expansion;

[tex](L + W)^4 = L^4 + 4L^3W + 6L^2W^2 + 4LW^3 + W^4[/tex]

So:

Solving (a): Winning at least 1

We look at the above and we list out the terms where the powers of W is at least 1; i.e., 1,2,3 and 4

So, we have:

[tex]Probability = 4L^3W + 6L^2W^2 + 4LW^3 + W^4[/tex]

Substitute value for W and L

[tex]Probability = 4 * 0.7^3*0.3 + 6*0.7^2*0.3^2 + 4*0.7*0.3^3 + 0.3^4[/tex]

[tex]Probability = 0.7599[/tex]

Hence, the probability of her winning at least one is 0.7599

Solving (a): Wining exactly 2

We look at the above and we list out the terms where the powers of W is exactly 2

So, we have:

[tex]Probability = 6L^2W^2[/tex]

Substitute value for W and L

[tex]Probability = 6*0.7^2*0.3^2[/tex]

[tex]Probability = 0.2646[/tex]

Hence, the probability of her winning exactly two is 0.2646

Answer:

The temperature and gravity both affects the density

Answer:wrong. Jts not velocity. Its period.

Explanation:

Took the test

Answer:

Th average force impact is [tex]F = 168.298 \ N[/tex]

Explanation:

From the question we are told that  

   The mass of the golf ball is  [tex]m_g = 26.7 \ g = 0.0267 \ kg[/tex]

    The angle made is [tex]\theta = 33.6 ^o[/tex]

    The range of the golf ball  is [tex]R = 190 \ m[/tex]

     The duration of contact is [tex]\Delta t = 7.13 \ ms = 7.13 *10^{-3} \ s[/tex]

Generally the range of the golf ball is mathematically represented as

       [tex]R = \frac{v^2 sin2(\theta)}{g}[/tex]

Here v  is the velocity with which the golf club propelled it with, making  v the subject

       [tex]v = \sqrt{\frac{R * g}{sin 2 (\theta)} }[/tex]

=>     [tex]v = \sqrt{\frac{190 * 9.8}{sin 2 (33.6)} }[/tex]

=>     [tex]v = 44.94 \ m/s[/tex]

Generally the change in momentum of the golf ball is mathematically represented as

      [tex]\Delta p = m * (v - u )[/tex]

here u  is the initial  velocity of the ball before being stroked and the value is 0 m/s

       [tex]\Delta p = 0.0267 * ( 44.94 - 0 )[/tex]

=>    [tex]\Delta p = 1.19996 \ kg \cdot m/s[/tex]

Generally the  average force of impact is mathematically represented as      

         [tex]F = \frac{\Delta p }{\Delta t}[/tex]

=>        [tex]F = \frac{1.19996 }{7.13 *10^{-3}}[/tex]

=>        [tex]F = 168.298 \ N[/tex]

Answer:

How long do you jump (sec) ?

Explanation:

The discovery of fossils remains of Cynognathus at both South America And Africa suggests that these continents used to be connected and later moved apart.

According to continental drift theory:

"All of the continents were once together as a single continent named Pangaea, which was surrounded by a Mega Ocean known as Panthalassa."

The continental drift theory was first proposed by Abraham Ortelius in 1596, and Alfred Wegener developed it in 1912.

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Answer:

b

Explanation:

i took the test

Earth’s landmasses were first recognized as the continents we know today

135 million years ago.

Landmass is defines as a large area of land. It can also be referred to as the

continents we have today. There are seven types of earth landmasses and

they are

They were first discovered around 135 million years ago by the early

dwellers of the earth.

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Answer:

C

Explanation:

There's a reason newton's 3rd law is called action-reaction :D

A - 1st law/inertia

B - 2nd law/f=ma

Newton's third law of motion states that for each action there is an equal and opposite reaction or force. Thus, the correct option is C.

Newton's third law of motion states that for every action or force applied in nature there is an equal and opposite reaction or force.

According to Newton's third law of Motion, if an object A exerts a force on the object B, then the object B must exert a force which is of equal magnitude and opposite direction back on the object A. This law represents symmetry in nature with the forces which are always occur in pairs, and one body cannot exert a force which is on another object without experiencing a force itself.

Therefore, the correct option is C.

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I feel like I'm in a city

Answer:

0.03 cm

Explanation: If the scale is 500:1, you have to divide 500 by 15 to get 0.03. You do not multiply 500 times 15 because the cells are smaller than the scale representation so you divide.

Answer:

A for sure

Explanation:

Answer:

D- Z, X, Y, W

Explanation:

Correct on edge

(a)to find voltage of battery we use the wire containg 4 ohm resistor and 3 ohm resistor

the voltage of 4ohm = Ri=4x1.5=6V

the voltage of 3 ohm = Ri=3x1.5=4.5v

since voltage is additive in series then Voltage of batteries = 4.5+6=10.5V

(b) the currrent flowing in 20 ohm resistor is the same as 8 ohm resistor so

Voltage of 8 ohm + voltage of 20 ohm= 10.5

8i+20i=10.5

28i=10.5

i=0.375 A

Answer:

–1652 N. The negative sign indicate that the force is in opposite direction to car.

Explanation:

The following data were obtained from the question:

Mass (m) of car = 1400 kg

Time (t) = 11 s

Initial velocity (u) = 25 m/s

Final velocity (v) = 12 m/s

Force (F) applied on the car =?

Next, we shall determine the acceleration of the car. This can be obtained as follow:

Time (t) = 11 s

Initial velocity (u) = 25 m/s

Final velocity (v) = 12 m/s

Acceleration (a) =?

a = (v – u) /t

a = (12 – 25) /11

a = –13/11

a = –1.18 m/s²

Finally, we shall determine the force on the car as follow:

Acceleration (a) = –1.18 m/s²

Mass (m) of car = 1400 kg

Force (F) applied on the car =?

F = ma

F = 1400 × –1.18

F = –1652 N

Thus, the force on the car is –1652 N. The negative sign indicate that the force is in opposite direction to car.

Answer:

False

Explanation:

Explanation:

Momentum is conserved when there is no net external force.  So momentum is conserved in the direction parallel to the incline.

p₀ = p

m v cos θ = (m + M) vₓ

vₓ = m v cos θ / (m + M)

After the collision, energy is conserved.

PE = KE

(m+M) gh = ½ (m+M) vₓ²

gh = ½ vₓ²

h = vₓ² / (2g)

d sin θ = [m v cos θ / (m + M)]² / (2g)

d = [m v cos θ / (m + M)]² / (2g sin θ)

Answer:

Moment of inertia = 0.3862kg-m²

Explanation:

2.00x10³

2.80cm

145 rad

r = r⊥ x F

F is an applied force

r⊥ is the distance between the applied force and axis

Force exerted = 2.00x10³

r⊥ = 2.8cm = 0.028m

Alpha = 145rad/s²

r = 0.028m x 2.00x10³

r = 56.0N-m

To get the moment of inertia

56.0N-m² = (145rad/s²) x I

The I would be:

I = (56.0N-m²)/(145rad/s²)

I = 56/145

= 0.3862Kg-m²

This is the moment of inertia.

Thank you!

Answer:

0.399 rev/s

Explanation:

Given that,

The diameter of a tornado, d = 74 m

Radius, r = 37 m

Linear velocity, v = 335 km/h = 93.05 m/s

We need to find the angular velocity in revolutions per second. Let it is [tex]\omega[/tex]. The relation between angular velocity and linear velocity is as follows :

[tex]v=r\omega\\\\\omega=\dfrac{v}{r}\\\\\omega=\dfrac{93.0556}{37}\\\\\omega=2.51\ rad/s[/tex]

or

[tex]\omega=\dfrac{2.51}{2\pi}\\\\\omega=0.399\ rev/s[/tex]

So, the angular velocity of the blade is 0.399 rev/s.

Answer:

I am 15th in my state for 55m hurdles with a time of 10.4 seconds

Explanation:

BAM

Answer: 44 m per minute

Explanation:

Answer:

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Explanation:

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Answer: 5cm

Explanation:

The cart comes to rest from 1.3 m/s in a matter of 0.30 s, so it undergoes an acceleration a of

a = (0 - 1.3 m/s) / (0.30 s)

a ≈ -4.33 m/s²

This acceleration is applied by a force of -65 N, i.e. a force of 65 N that opposes the cart's motion downhill. So the cart has a mass m such that

-65 N = m (-4.33 m/s²)

m = 15 kg

Answer:

(a) V₂ = 1.86 m/s

(b) Q = 5.1 x 10⁻⁴ m³/s

Explanation:

(a)

The formula derived for Venturi tube is as follows:

P₁ - P₂ = (ρ/2)(V₂² - V₁²)

where,

P₁ - P₂ = Difference in Pressure of Inlet and Outlet = 1.2 KPa = 1200 Pa

ρ = Density of Gasoline = 7.4 x 10² kg/m³

V₂ = Exit Velocity = ?

V₁ = Inlet Velocity

Therefore,

1200 Pa = [(7.4 x 10²kg/m³)/2](V₂² - V₁²)

V₂² - V₁² = (1200 Pa)/(3.7 x 10² kg/m³)

V₂² - V₁² = 3.24 m²/s²   ------------------- equation (1)

Now, we will use continuity equation:

A₁V₁ = A₂V₂

where,

A₁ = Inlet Area = πd₁²/4 = π(0.0374 m)²/4 = 1.098 x 10⁻³ m²

A₂ = Exit Area = πd₂²/4 = π(0.0187 m)²/4 = 2.746 x 10⁻⁴ m²

Therefore,

(1.098 x 10⁻³ m²)V₁ = (2.746 x 10⁻⁴ m²)V₂

V₁ = (2.746 x 10⁻⁴ m²)V₂/(1.098 x 10⁻³ m²)

V₁ = 0.25 V₂  

using this value in equation (1):

V₂² - (0.25 V₂)² = 3.24 m²/s²

0.9375 V₂² = 3.24 m²/s²

V₂² = (3.24 m²/s²)/0.9375

V₂ = √(3.456 m²/s²)

V₂ = 1.86 m/s

(b)

For fluid flow rate we use the following equation:

Flow Rate = Q = A₂V₂ = (2.746 x 10⁻⁴ m²)(1.86 m/s)

Q = 5.1 x 10⁻⁴ m³/s

The formula for finding variables in a  Venturi tube is shown below:

P₁ - P₂ = (ρ/2)(V₂² - V₁²)

where, P₁ - P₂ is difference in pressure of Inlet and outlet, ρ = density, V₂ = exit velocity and V₁ is inlet velocity

P₁ - P₂ = 1.2 KPa = 1200 Pa

ρ = 7.4 x 10² kg/m³

V₂ = Exit Velocity = ?

V₁ = Inlet Velocity

We then substitute the variables into this equation.

P₁ - P₂ = (ρ/2)(V₂² - V₁²)

1200 Pa = [(7.4 x 10²kg/m³)/2](V₂² - V₁²)

V₂² - V₁² = (1200 Pa)/(3.7 x 10² kg/m³)

V₂² - V₁² = 3.24 m²/s²  ------ equation (1)

The  continuity equation A₁V₁ = A₂V₂ is then used

where,A₁ = Inlet area = πd₁²/4 = π(0.0374 m)²/4 = 1.098 x 10⁻³ m²

A₂ = Exit Area = πd₂²/4 = π(0.0187 m)²/4 = 2.746 x 10⁻⁴ m²

(1.098 x 10⁻³ m²)V₁ = (2.746 x 10⁻⁴ m²)V₂

V₁ = (2.746 x 10⁻⁴ m²)V₂/(1.098 x 10⁻³ m²)

V₁ = 0.25 V₂  

We then substitute the value into equation 1

V₂² - (0.25 V₂)² = 3.24 m²/s²

0.9375 V₂² = 3.24 m²/s²

V₂² = (3.24 m²/s²)/0.9375

V₂ = √(3.456 m²/s²)

V₂ = 1.86 m/s

This can be calculated using the formula

Flow Rate = Q = A₂V₂

                  = (2.746 x 10⁻⁴ m²)(1.86 m/s)

                 = 5.1 x 10⁻⁴ m³/s

Answer:

(a) Normal force=7.48 N

Explanation:

N+F~1 sinθ-mg=0

=>N=1.5*9.8-12 sin37◦

=>N=14.7-7.22=7.48 N