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4 years ago

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A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track

at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?(A) 0.5< t < 0.75 (B) 1.75< t < 2.0 (C) 2.0 < t < 2.5 (D) 2.5 < t < 3.0 (E) 3 < t < 3.5

1 answer:

Taya2010 [7]4 years ago

7 0

Answer:

The number of hours is 2.1.

(c) is a correct statement.

Explanation:

Given that,

Diameter = 2 miles

Average rate = 3 miles/hr

We need to calculate the time

Using formula of average rate

$Average\ rate =\dfrac{Total\ distance}{Total\ time}$

Put the value into the formula

$3=\dfrac{2\pi\times r}{t}$

$t=\dfrac{6.28}{3}$

$t = 2.1\ hr$

2.1 lies between 2.0 and 2.5.

Hence, The number of hours is 2.1.

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3. Three blocks of masses m, 2m and 3m are suspended from the ceiling using ropes as shown in diagram. Which of the following co

Alja [10]

Answer:

The correct option is d: T₁ > T₂ > T₃.

Explanation:

Let's evaluate each tension.

<u>Case T₃.</u>

$T_{3} - W_{3} = 0$

For the system to be in equilibrium, the algebraic sum of the tension force (T) and the weight (W) must be equal to zero. The minus sign of W is because it is in the opposite direction of T.

$T_{3} = W_{3}$

Since W₃ = mg, where <em>m</em> is for mass and <em>g</em> is for the acceleration due to gravity, we have:

$T_{3} = W_{3} = mg$ (1) <u>Case T₂.</u>

$T_{2} - (T_{3} + W_{2}) = 0$

$T_{2} = T_{3} + W_{2}$ (2)

By entering W₂ = 2mg and equation (1) into eq (2) we have:

$T_{2} = T_{3} + W_{2} = mg + 2mg = 3mg$

<u>Case T₁.</u>

$T_{1} - (T_{2} + W_{1}) = 0$

$T_{1} = T_{2} + W_{1}$ (3)

Knowing that W₁ = 3mg and T₂ = 3mg, eq (3) is:

$T_{1} = 3mg + 3mg = 6mg$

Therefore, the correct option is d: T₁ > T₂ > T₃.

I hope it helps you!

6 0

3 years ago

Read 2 more answers

Tarzan, who weighs 849 N, swings from a cliff at the end of a 18.0 m vine that hangs from a high tree limb and initially makes a

loris [4]

Answer:

Part a)

$T = 342.5 \hat i + 675\hat j$

Part b)

$F_{net} = 342.5\hat i - 174\hat j$

Part c)

$F = 384.2 N$

Part d)

$\theta = 333 degree$

Part e)

$a = 4.4 m/s^2$

Part f)

$\theta = 333 degree$

Explanation:

Part a)

Magnitude of tension force is given as

$T = 757 N$ at 26.9 degree with vertical

$T = 757 sin26.9 \hat i + 757 cos26.9 \hat j$

$T = 342.5 \hat i + 675\hat j$

Part b)

Net force on Tarzen is given as

$F_{net} = T + F_g$

$F_{net} = 342.5 \hat i + 675\hat j - 849 \hat j$

$F_{net} = 342.5\hat i - 174\hat j$

Part c)

magnitude of the force is given as

$F = \sqrt{F_x^2 + F_y^2}$

$F = \sqrt{342.5^2 + 174^2}$

$F = 384.2 N$

Part d)

Direction of the force is given as

$tan\theta = \frac{F_y}{F_x}$

$tan\theta = \frac{-174}{342.5}$

$\theta = 333 degree$

Part e)

Magnitude of the acceleration

$a = \frac{F}{m}$

$m = \frac{849}{9.81} = 86.5 kg$

tex]a = \frac{384.2}{86.5}[/tex]

$a = 4.4 m/s^2$

Part f)

Direction of acceleration is same as the direction of the force

$\theta = 333 degree$

6 0

3 years ago

A 1.00 x 109 kg object is raised vertically at a

DerKrebs [107]

Answer:

P = 3.92 10¹⁰ W

Explanation:

The power is data by the expression

P = W / t

the work of a force is

W = F. y

the bold ones represent vectors. In this case the displacement is vertical upwards and the vertical forces upwards, therefore the angle is zero and the cos 0 = 1

W = F y

we substitute

P = F y / t

P = F v

as the body rises at constant speed the acceleration is zero and from the equilibrium condition

F -W = 0

F = mg

we substitute

P = m g v

let's calculate

P 1.00 10⁹ 9.8 4

P = 3.92 10¹⁰ W

5 0

3 years ago

Which property is useful for describing a substance might depend on the state of matter the substance is in?

Sliva [168]

The amount of energy in molecules of matter determines the state of matter. Matter can exist in one of several different states, including a gas, liquid, or solid state.

7 0

3 years ago

Read 2 more answers

A skateboarder initially has 5 kJ of kinetic energy. As she freewheels along a flat section of path, she does 400 J of work agai

sweet [91]

The final kinetic energy of the skateboarder after she freewheels and did work against friction on the flat section of the path is 4,600 J.

<h3>Conservation of energy</h3>

The final kinetic energy of the stakeboarder is determined by applying the principle of conservation of energy as shown below;

ΔK.E = -W

K.Ef - K.Ei = -W

where;

K.Ef is the final kinetic energy
K.Ei is the initial kinetic energy
W is work done

K.Ef = K.Ei - W

K.Ef = 5,000 J - 400 J

K.Ef = 4,600 J

Thus, the final kinetic energy of the skateboarder is 4,600 J.

Learn more about kinetic energy here: brainly.com/question/25959744

4 0

2 years ago