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kenny6666 [7]
3 years ago
14

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
Physics
1 answer:
Taya2010 [7]3 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 years ago
Two remote control cars with masses of 1.16 kilograms and 1.98 kilograms travel toward each other at speeds of 8.64 meters per s
Black_prince [1.1K]

The initial momentum of the system can be expressed as,

p_i=m_1u_1+m_{2_{}}u_2

The final momentum of the system can be given as,

p_f=m_1v_1+m_{2_{}}v_2

According to conservation of momentum,

p_i=p_f

Plug in the known expressions,

\begin{gathered} m_1u_1+m_2u_2=m_1v_1+m_2v_2 \\ m_2v_2=m_1u_1+m_2u_2-m_1v_1 \\ v_2=\frac{m_1u_1+m_2u_2-m_1v_1}{m_2} \end{gathered}

Initially, the second mass move towards the first mass therefore the initial speed of second mass will be taken as negative and the recoil velocity of first mass is also taken as negative.

Plug in the known values,

\begin{gathered} v_2=\frac{(1.16\text{ kg)(8.64 m/s)+(1.98 kg)(-3.34 m/s)-(1.16 kg)(-2.16 m/s)}}{1.98\text{ kg}} \\ =\frac{10.02\text{ kgm/s-}6.61\text{ kgm/s+}2.51\text{ kgm/s}}{1.98\text{ kg}} \\ =\frac{5.92\text{ kgm/s}}{1.98\text{ kg}} \\ \approx2.99\text{ m/s} \end{gathered}

Thus, the final velocity of second mass is 2.99 m/s.

3 0
1 year ago
Which statement explains the similarity between momentum and kinetic energy of an object?
Anon25 [30]

Answer:B.

Both increase as the mass and velocity increase.

3 0
3 years ago
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Two trains are traveling side-by-side along parallel, straight tracks at the same speed. In a time t, train A doubles its speed.
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Answer:

derdddrdickdd

Explanation:

3 0
3 years ago
What is the direction of the field halfway between two horizontal parallel wires if the top wire has a current of 4 A to the lef
Alex777 [14]

Answer:

A) Out of the page.

Explanation:

Right-hand rule points the direction of the magnetic field at any point.

<u>Top wire</u>: Current is to the left. Point your thumb to the left and curl your other fingers around the wire. The tips of the four fingers points the direction of the field at that point. In this case, out of the page.

<u>Bottom wire</u>: Current is to the right. Point your thumb to the right and curl your other fingers around the wire. The tips of the four finger points out of the page again.

So, the total field produced by both wires is directed out of the page.

Another method to figure out the direction is the mathematical method.

Use the B-field formula:

d\vec{B} = \frac{\mu_0}{4\pi}\frac{Id\vec{l}\times \^r}{r^2}

The cross product between the direction of the current and the target position gives the direction of the B-field. If the left is -x direction and downwards is the -y direction, then

(-\^x) \times (-\^y) = +\^z for the top wire.

(+\^x) \times (+\^y) = +\^z for the bottom wire.

4 0
3 years ago
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